पहचान ( (a+b)2 ) का सही विस्तार क्या है?
What is the correct expansion of the identity ( (a+b)2 )?
#algebraic identities
#square identity
#binomial
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A \(a^2+b^2\) / only square terms
B \(a^2+2ab+b^2\) / correct expansion
C \(a^2-ab+b^2\) / middle term negative
D (2a+2b) / double of terms
Explanation opens after your attempt
Correct Answer
B. \(a^2+2ab+b^2\) / correct expansion
Step 1
Concept
In ( (a+b)2 ), the middle term is (2ab). Exam tip: do not forget the middle term in square identities.
Step 2
Why this answer is correct
The correct answer is B. \(a^2+2ab+b^2\) / correct expansion. In ( (a+b)2 ), the middle term is (2ab). Exam tip: do not forget the middle term in square identities.
Step 3
Exam Tip
( (a+b)2 ) में बीच का पद (2ab) आता है। परीक्षा में वर्ग पहचान में मध्य पद न भूलें।
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पहचान ( (x-y)2 ) का सही विस्तार चुनिए।
Choose the correct expansion of the identity ( (x-y)2 ).
#algebraic identities
#minus square
#binomial
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A \(x^2+2xy+y^2\) / plus middle term
B \(x^2-y^2\) / difference only
C \(x^2-2xy+y^2\) / correct expansion
D \(x^2+xy-y^2\) / mixed signs
Explanation opens after your attempt
Correct Answer
C. \(x^2-2xy+y^2\) / correct expansion
Step 1
Concept
In ( (x-y)2 ), the middle term is (-2xy). Exam tip: pay attention to the negative sign.
Step 2
Why this answer is correct
The correct answer is C. \(x^2-2xy+y^2\) / correct expansion. In ( (x-y)2 ), the middle term is (-2xy). Exam tip: pay attention to the negative sign.
Step 3
Exam Tip
( (x-y)2 ) में बीच का पद (-2xy) होता है। परीक्षा में ऋण चिह्न पर ध्यान दें।
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पहचान ( (p+q)(p-q) ) किसके बराबर होती है?
The identity ( (p+q)(p-q) ) is equal to what?
#difference of squares
#identity
#algebra
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A \(p^2-q^2\) / difference of squares
B \(p^2+q^2\) / sum of squares
C \(p^2+2pq+q^2\) / square of sum
D \(p^2-2pq+q^2\) / square of difference
Explanation opens after your attempt
Correct Answer
A. \(p^2-q^2\) / difference of squares
Step 1
Concept
( (p+q)(p-q)=p-2 -q-2 ). Exam tip: remember it as difference of squares.
Step 2
Why this answer is correct
The correct answer is A. \(p^2-q^2\) / difference of squares. ( (p+q)(p-q)=p-2 -q-2 ). Exam tip: remember it as difference of squares.
Step 3
Exam Tip
( (p+q)(p-q)=p-2 -q-2 ) होता है। परीक्षा में इसे वर्गों का अंतर याद रखें।
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( (m+n)2 ) में (2mn) को क्या कहा जा सकता है?
In ( (m+n)2 ), what can (2mn) be called?
#middle term
#binomial square
#identity
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A पहला वर्ग / first square
B दूसरा वर्ग / second square
C स्थिर पद / constant term
D मध्य पद / middle term
Explanation opens after your attempt
Correct Answer
D. मध्य पद / middle term
Step 1
Concept
In ( (m+n)2 =m-2 +2mn+n-2 ), (2mn) is the middle term. Exam tip: identify all three terms.
Step 2
Why this answer is correct
The correct answer is D. मध्य पद / middle term. In ( (m+n)2 =m-2 +2mn+n-2 ), (2mn) is the middle term. Exam tip: identify all three terms.
Step 3
Exam Tip
( (m+n)2 =m-2 +2mn+n-2 ) में (2mn) मध्य पद है। परीक्षा में तीन पदों की पहचान करें।
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( (7+3)2 ) को पहचान से निकालने पर मान क्या होगा?
Using an identity, what is the value of ( (7+3)2 )?
#numerical identity
#square
#mental math
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A (70)
B (100)
C (49)
D (60)
Explanation opens after your attempt
Step 1
Concept
( (7+3)2 =102 =100 ). Exam tip: identities make mental calculation faster.
Step 2
Why this answer is correct
The correct answer is B. (100). ( (7+3)2 =102 =100 ). Exam tip: identities make mental calculation faster.
Step 3
Exam Tip
( (7+3)2 =102 =100 ) होता है। परीक्षा में पहचान से मानसिक गणना तेज होती है।
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( (10-2)2 ) का मान कौन-सा है?
What is the value of ( (10-2)2 )?
#numerical square
#algebraic identities
#easy
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A (144)
B (100)
C (64)
D (80)
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Step 1
Concept
( (10-2)2 =82 =64 ). Exam tip: first find the value inside the bracket.
Step 2
Why this answer is correct
The correct answer is C. (64). ( (10-2)2 =82 =64 ). Exam tip: first find the value inside the bracket.
Step 3
Exam Tip
( (10-2)2 =82 =64 ) होता है। परीक्षा में पहले कोष्ठक का मान निकालें।
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\( 15^2-5^2 \) को किस पहचान से सरल किया जा सकता है?
Which identity can simplify \( 15^2-5^2 \)?
#difference of squares
#numerical identity
#factorisation
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A ( (a+b)2 )
B ( (a-b)2 )
C \(a^2+b^2\)
D (a-2 -b-2 =(a+b)(a-b))
Explanation opens after your attempt
Correct Answer
D. (a-2 -b-2 =(a+b)(a-b))
Step 1
Concept
This is the form \(a^2-b^2\). Exam tip: convert difference of squares into a product.
Step 2
Why this answer is correct
The correct answer is D. (a-2 -b-2 =(a+b)(a-b)). This is the form \(a^2-b^2\). Exam tip: convert difference of squares into a product.
Step 3
Exam Tip
यह \(a^2-b^2\) का रूप है। परीक्षा में वर्गों के अंतर को गुणनफल में बदलें।
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( (x+4)2 ) का विस्तार क्या होगा?
What is the expansion of ( (x+4)2 )?
#expansion
#binomial square
#x plus number
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A \(x^2+8x+16\)
B \(x^2+4x+16\)
C \(x^2+16x+4\)
D \(x^2-8x+16\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+8x+16\)
Step 1
Concept
( (x+4)2 =x-2 +2\cdot x\cdot4+16=x-2 +8x+16 ). Exam tip: use (2ab).
Step 2
Why this answer is correct
The correct answer is A. \(x^2+8x+16\). ( (x+4)2 =x-2 +2\cdot x\cdot4+16=x-2 +8x+16 ). Exam tip: use (2ab).
Step 3
Exam Tip
( (x+4)2 =x-2 +2\cdot x\cdot4+16=x-2 +8x+16 )। परीक्षा में (2ab) लगाएँ।
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( (y-5)2 ) का सही विस्तार चुनिए।
Choose the correct expansion of ( (y-5)2 ).
#expansion
#minus square
#y minus number
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A \(y^2+10y+25\)
B \(y^2-10y+25\)
C \(y^2-5y+25\)
D \(y^2-25\)
Explanation opens after your attempt
Correct Answer
B. \(y^2-10y+25\)
Step 1
Concept
( (y-5)2 =y-2 -10y+25 ). Exam tip: keep the sign of the middle term correct.
Step 2
Why this answer is correct
The correct answer is B. \(y^2-10y+25\). ( (y-5)2 =y-2 -10y+25 ). Exam tip: keep the sign of the middle term correct.
Step 3
Exam Tip
( (y-5)2 =y-2 -10y+25 ) होता है। परीक्षा में मध्य पद का चिह्न सही रखें।
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( (3a+2b)2 ) में मध्य पद क्या है?
What is the middle term in ( (3a+2b)2 )?
#middle term
#binomial square
#algebra
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A (6ab)
B \(9a^2\)
C (12ab)
D \(4b^2\)
Explanation opens after your attempt
Step 1
Concept
The middle term is \(2\cdot3a\cdot2b=12ab\). Exam tip: multiply both terms and then multiply by (2).
Step 2
Why this answer is correct
The correct answer is C. (12ab). The middle term is \(2\cdot3a\cdot2b=12ab\). Exam tip: multiply both terms and then multiply by (2).
Step 3
Exam Tip
मध्य पद \(2\cdot3a\cdot2b=12ab\) है। परीक्षा में दोनों पदों को गुणा करके (2) से गुणा करें।
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( (2x-3)2 ) का विस्तार क्या है?
What is the expansion of ( (2x-3)2 )?
#expansion
#binomial square
#negative middle term
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A \(4x^2+12x+9\)
B \(2x^2-6x+9\)
C \(4x^2-6x+9\)
D \(4x^2-12x+9\)
Explanation opens after your attempt
Correct Answer
D. \(4x^2-12x+9\)
Step 1
Concept
( (2x-3)2 =4x-2 -12x+9 ). Exam tip: remember (-2ab).
Step 2
Why this answer is correct
The correct answer is D. \(4x^2-12x+9\). ( (2x-3)2 =4x-2 -12x+9 ). Exam tip: remember (-2ab).
Step 3
Exam Tip
( (2x-3)2 =4x-2 -12x+9 ) होता है। परीक्षा में (-2ab) का ध्यान रखें।
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( (a+6)(a-6) ) किसके बराबर है?
What is ( (a+6)(a-6) ) equal to?
#difference of squares
#factor product
#identity
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A \(a^2-36\)
B \(a^2+36\)
C \(a^2+12a+36\)
D \(a^2-12a+36\)
Explanation opens after your attempt
Correct Answer
A. \(a^2-36\)
Step 1
Concept
( (a+6)(a-6)=a-2 -62 =a-2 -36 ). Exam tip: remember \(6^2=36\).
Step 2
Why this answer is correct
The correct answer is A. \(a^2-36\). ( (a+6)(a-6)=a-2 -62 =a-2 -36 ). Exam tip: remember \(6^2=36\).
Step 3
Exam Tip
( (a+6)(a-6)=a-2 -62 =a-2 -36 )। परीक्षा में \(6^2=36\) याद रखें।
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( (x+2)(x+3) ) को सरल करने का सही परिणाम क्या है?
What is the correct simplified result of ( (x+2)(x+3) )?
#product identity
#x plus a
#x plus b
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A \(x^2+5x+5\)
B \(x^2+5x+6\)
C \(x^2+6x+5\)
D \(x^2+2x+3\)
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Correct Answer
B. \(x^2+5x+6\)
Step 1
Concept
( (x+2)(x+3)=x-2 +5x+6 ). Exam tip: take product (6) and sum (5) of constants.
Step 2
Why this answer is correct
The correct answer is B. \(x^2+5x+6\). ( (x+2)(x+3)=x-2 +5x+6 ). Exam tip: take product (6) and sum (5) of constants.
Step 3
Exam Tip
( (x+2)(x+3)=x-2 +5x+6 ) होता है। परीक्षा में स्थिर पदों का गुणन (6) और योग (5) लें।
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( (x+1)(x+7) ) में (x) का गुणांक क्या होगा?
What will be the coefficient of (x) in ( (x+1)(x+7) )?
#coefficient
#product identity
#algebra
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A (7)
B (1)
C (8)
D (6)
Explanation opens after your attempt
Step 1
Concept
In ( (x+1)(x+7)=x-2 +8x+7 ), the coefficient of (x) is (8). Exam tip: add the constants.
Step 2
Why this answer is correct
The correct answer is C. (8). In ( (x+1)(x+7)=x-2 +8x+7 ), the coefficient of (x) is (8). Exam tip: add the constants.
Step 3
Exam Tip
( (x+1)(x+7)=x-2 +8x+7 ) में (x) का गुणांक (8) है। परीक्षा में स्थिर पदों का योग लें।
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( (t-4)(t+4) ) का परिणाम क्या है?
What is the result of ( (t-4)(t+4) )?
#difference of squares
#t variable
#identity
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A \(t^2+16\)
B \(t^2-8t+16\)
C \(t^2+8t+16\)
D \(t^2-16\)
Explanation opens after your attempt
Correct Answer
D. \(t^2-16\)
Step 1
Concept
( (t-4)(t+4)=t-2 -16 ). Exam tip: use difference of squares for opposite signs.
Step 2
Why this answer is correct
The correct answer is D. \(t^2-16\). ( (t-4)(t+4)=t-2 -16 ). Exam tip: use difference of squares for opposite signs.
Step 3
Exam Tip
( (t-4)(t+4)=t-2 -16 ) होता है। परीक्षा में विपरीत चिह्नों पर वर्गों का अंतर लगाएँ।
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\( 99^2 \) को आसानी से निकालने के लिए कौन-सा रूप सबसे अच्छा है?
Which form is best for finding \( 99^2 \) easily?
#mental math
#square identity
#99 square
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A ( (100-1)2 )
B ( (90+9)3 )
C ( (50+49) )
D ( (99+1)(99-1) )
Explanation opens after your attempt
Correct Answer
A. ( (100-1)2 )
Step 1
Concept
(992 =(100-1)2 ) is easy to use. Exam tip: use a nearby round number.
Step 2
Why this answer is correct
The correct answer is A. ( (100-1)2 ). (992 =(100-1)2 ) is easy to use. Exam tip: use a nearby round number.
Step 3
Exam Tip
(992 =(100-1)2 ) से आसानी से निकलेगा। परीक्षा में निकट पूर्ण संख्या का उपयोग करें।
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\( 101^2 \) के लिए पहचान ( (a+b)2 ) में (a) और (b) क्या लिए जा सकते हैं?
For \( 101^2 \), what can be taken as (a) and (b) in ( (a+b)2 )?
#mental math
#101 square
#algebraic identity
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A (a=99), (b=2)
B (a=100), (b=1)
C (a=101), (b=0)
D (a=50), (b=51)
Explanation opens after your attempt
Correct Answer
B. (a=100), (b=1)
Step 1
Concept
Since (101=100+1), taking (a=100) and (b=1) is easy. Exam tip: choose an easy split.
Step 2
Why this answer is correct
The correct answer is B. (a=100), (b=1). Since (101=100+1), taking (a=100) and (b=1) is easy. Exam tip: choose an easy split.
Step 3
Exam Tip
(101=100+1) इसलिए (a=100) और (b=1) लेना आसान है। परीक्षा में आसान विभाजन चुनें।
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( (5x)2 ) का मान क्या है?
What is the value of ( (5x)2 )?
#square of monomial
#coefficient
#x square
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A \(5x^2\)
B \(10x^2\)
C \(25x^2\)
D (25x)
Explanation opens after your attempt
Correct Answer
C. \(25x^2\)
Step 1
Concept
( (5x)2 =25x-2 ). Exam tip: square both the coefficient and the variable.
Step 2
Why this answer is correct
The correct answer is C. \(25x^2\). ( (5x)2 =25x-2 ). Exam tip: square both the coefficient and the variable.
Step 3
Exam Tip
( (5x)2 =25x-2 ) होता है। परीक्षा में गुणांक और चर दोनों का वर्ग करें।
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( (2a+5)2 ) में पहला पद कौन-सा होगा?
What will be the first term in ( (2a+5)2 )?
#first term
#binomial square
#2a plus 5
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A \(2a^2\)
B (10a)
C (25)
D \(4a^2\)
Explanation opens after your attempt
Correct Answer
D. \(4a^2\)
Step 1
Concept
The first term is ( (2a)2 =4a-2 ). Exam tip: square the complete first term.
Step 2
Why this answer is correct
The correct answer is D. \(4a^2\). The first term is ( (2a)2 =4a-2 ). Exam tip: square the complete first term.
Step 3
Exam Tip
पहला पद ( (2a)2 =4a-2 ) होगा। परीक्षा में पहले पद का पूरा वर्ग करें।
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( (3x+1)2 ) का सही विस्तार क्या है?
What is the correct expansion of ( (3x+1)2 )?
#expansion
#3x plus 1
#binomial square
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A \(9x^2+6x+1\)
B \(3x^2+6x+1\)
C \(9x^2+3x+1\)
D \(9x^2+1\)
Explanation opens after your attempt
Correct Answer
A. \(9x^2+6x+1\)
Step 1
Concept
( (3x+1)2 =9x-2 +6x+1 ). Exam tip: write \(2\cdot3x\cdot1=6x\).
Step 2
Why this answer is correct
The correct answer is A. \(9x^2+6x+1\). ( (3x+1)2 =9x-2 +6x+1 ). Exam tip: write \(2\cdot3x\cdot1=6x\).
Step 3
Exam Tip
( (3x+1)2 =9x-2 +6x+1 ) होता है। परीक्षा में \(2\cdot3x\cdot1=6x\) लिखें।
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( (x-9)2 ) में स्थिर पद कौन-सा है?
What is the constant term in ( (x-9)2 )?
#constant term
#x minus 9
#square identity
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A (9)
B (81)
C (-18x)
D \(x^2\)
Explanation opens after your attempt
Step 1
Concept
In ( (x-9)2 =x-2 -18x+81 ), the constant term is (81). Exam tip: square the last term.
Step 2
Why this answer is correct
The correct answer is B. (81). In ( (x-9)2 =x-2 -18x+81 ), the constant term is (81). Exam tip: square the last term.
Step 3
Exam Tip
( (x-9)2 =x-2 -18x+81 ) में स्थिर पद (81) है। परीक्षा में अंतिम पद का वर्ग करें।
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( (4a-b)2 ) में मध्य पद क्या होगा?
What is the middle term in ( (4a-b)2 )?
#middle term
#4a minus b
#identity
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A (8ab)
B (4ab)
C (-8ab)
D (-4ab)
Explanation opens after your attempt
Step 1
Concept
The middle term is \(-2\cdot4a\cdot b=-8ab\). Exam tip: apply (2ab) with the negative sign.
Step 2
Why this answer is correct
The correct answer is C. (-8ab). The middle term is \(-2\cdot4a\cdot b=-8ab\). Exam tip: apply (2ab) with the negative sign.
Step 3
Exam Tip
मध्य पद \(-2\cdot4a\cdot b=-8ab\) है। परीक्षा में ऋण चिह्न सहित (2ab) लगाएँ।
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\( 51^2 \) को ( (50+1)2 ) से निकालने पर परिणाम क्या है?
Using ( (50+1)2 ), what is \( 51^2 \)?
#mental calculation
#51 square
#identity
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A (2501)
B (2600)
C (2500)
D (2601)
Explanation opens after your attempt
Step 1
Concept
\(51^2=2500+100+1=2601\). Exam tip: add (2ab) separately.
Step 2
Why this answer is correct
The correct answer is D. (2601). \(51^2=2500+100+1=2601\). Exam tip: add (2ab) separately.
Step 3
Exam Tip
\(51^2=2500+100+1=2601\) होता है। परीक्षा में (2ab) को अलग से जोड़ें।
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\( 48^2 \) को किस रूप में लिखकर आसानी से निकाला जा सकता है?
Which form can be used to find \( 48^2 \) easily?
#mental math
#48 square
#minus identity
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A ( (50-2)2 )
B ( (40+8)3 )
C ( (48+2)(48-2) )
D (48+48)
Explanation opens after your attempt
Correct Answer
A. ( (50-2)2 )
Step 1
Concept
Since (48=50-2), ( (50-2)2 ) is useful. Exam tip: write it using a nearby larger number.
Step 2
Why this answer is correct
The correct answer is A. ( (50-2)2 ). Since (48=50-2), ( (50-2)2 ) is useful. Exam tip: write it using a nearby larger number.
Step 3
Exam Tip
(48=50-2) इसलिए ( (50-2)2 ) उपयोगी है। परीक्षा में निकट बड़ी संख्या से घटाकर लिखें।
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( (a+b)2 -(a-b)2 ) का सरल रूप क्या है?
What is the simplified form of ( (a+b)2 -(a-b)2 )?
#identity comparison
#simplification
#4ab
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A \(2a^2+2b^2\)
B (4ab)
C \(a^2-b^2\)
D (2ab)
Explanation opens after your attempt
Step 1
Concept
After subtracting both expansions, (4ab) remains. Exam tip: expand first and cancel like terms.
Step 2
Why this answer is correct
The correct answer is B. (4ab). After subtracting both expansions, (4ab) remains. Exam tip: expand first and cancel like terms.
Step 3
Exam Tip
दोनों विस्तार घटाने पर (4ab) बचता है। परीक्षा में पहले विस्तार करके समान पद काटें।
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( (x+5)2 -(x-5)2 ) का मान क्या होगा?
What is the value of ( (x+5)2 -(x-5)2 )?
#simplification
#identity
#20x
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A (10x)
B (25x)
C (20x)
D (100)
Explanation opens after your attempt
Step 1
Concept
This is ( (a+b)2 -(a-b)2 =4ab ), so \(4\cdot x\cdot5=20x\). Exam tip: apply the identity directly.
Step 2
Why this answer is correct
The correct answer is C. (20x). This is ( (a+b)2 -(a-b)2 =4ab ), so \(4\cdot x\cdot5=20x\). Exam tip: apply the identity directly.
Step 3
Exam Tip
यह ( (a+b)2 -(a-b)2 =4ab ) है, इसलिए \(4\cdot x\cdot5=20x\)। परीक्षा में पहचान सीधे लगाएँ।
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( (a+b)2 +(a-b)2 ) का सरल रूप कौन-सा है?
Which is the simplified form of ( (a+b)2 +(a-b)2 )?
#sum of identities
#binomial square
#simplification
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A (4ab)
B (2ab)
C \(a^2+b^2\)
D \(2a^2+2b^2\)
Explanation opens after your attempt
Correct Answer
D. \(2a^2+2b^2\)
Step 1
Concept
Adding both expansions cancels middle terms and gives \(2a^2+2b^2\). Exam tip: add like terms.
Step 2
Why this answer is correct
The correct answer is D. \(2a^2+2b^2\). Adding both expansions cancels middle terms and gives \(2a^2+2b^2\). Exam tip: add like terms.
Step 3
Exam Tip
दोनों विस्तार जोड़ने पर मध्य पद कटते हैं और \(2a^2+2b^2\) मिलता है। परीक्षा में समान पद जोड़ें।
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( (2x+3y)2 ) में अंतिम पद कौन-सा है?
What is the last term in ( (2x+3y)2 )?
#last term
#2x plus 3y
#square identity
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A \(9y^2\)
B (6xy)
C \(4x^2\)
D (12xy)
Explanation opens after your attempt
Correct Answer
A. \(9y^2\)
Step 1
Concept
The last term is ( (3y)2 =9y-2 ). Exam tip: square the complete term.
Step 2
Why this answer is correct
The correct answer is A. \(9y^2\). The last term is ( (3y)2 =9y-2 ). Exam tip: square the complete term.
Step 3
Exam Tip
अंतिम पद ( (3y)2 =9y-2 ) है। परीक्षा में हर पद का पूरा वर्ग करें।
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( (2x+3y)2 ) का मध्य पद क्या होगा?
What is the middle term of ( (2x+3y)2 )?
#middle term
#2x plus 3y
#algebraic identity
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A (5xy)
B (12xy)
C (6xy)
D (10xy)
Explanation opens after your attempt
Step 1
Concept
The middle term is \(2\cdot2x\cdot3y=12xy\). Exam tip: multiply first and then multiply by (2).
Step 2
Why this answer is correct
The correct answer is B. (12xy). The middle term is \(2\cdot2x\cdot3y=12xy\). Exam tip: multiply first and then multiply by (2).
Step 3
Exam Tip
मध्य पद \(2\cdot2x\cdot3y=12xy\) है। परीक्षा में पहले गुणा फिर (2) से गुणा करें।
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( (m+4)(m+6) ) का विस्तार क्या है?
What is the expansion of ( (m+4)(m+6) )?
#product identity
#m plus numbers
#expansion
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A \(m^2+10m+24\)
B \(m^2+24m+10\)
C \(m^2+2m+24\)
D \(m^2+10m+10\)
Explanation opens after your attempt
Correct Answer
A. \(m^2+10m+24\)
Step 1
Concept
( (m+4)(m+6)=m-2 +10m+24 ). Exam tip: take (4+6=10) and \(4\cdot6=24\).
Step 2
Why this answer is correct
The correct answer is A. \(m^2+10m+24\). ( (m+4)(m+6)=m-2 +10m+24 ). Exam tip: take (4+6=10) and \(4\cdot6=24\).
Step 3
Exam Tip
( (m+4)(m+6)=m-2 +10m+24 ) होता है। परीक्षा में (4+6=10) और \(4\cdot6=24\) लें।
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( (x-2)(x-5) ) में स्थिर पद क्या है?
What is the constant term in ( (x-2)(x-5) )?
#constant term
#product identity
#negative constants
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A (-7)
B (10)
C (-10)
D (7)
Explanation opens after your attempt
Step 1
Concept
The constant term is ((-2)(-5)=10). Exam tip: remember negative times negative is positive.
Step 2
Why this answer is correct
The correct answer is B. (10). The constant term is ((-2)(-5)=10). Exam tip: remember negative times negative is positive.
Step 3
Exam Tip
स्थिर पद ((-2)(-5)=10) होता है। परीक्षा में ऋण गुणा ऋण धन याद रखें।
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( (x-2)(x-5) ) में (x) का गुणांक क्या है?
What is the coefficient of (x) in ( (x-2)(x-5) )?
#coefficient
#product identity
#x minus numbers
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A (7)
B (10)
C (-7)
D (-10)
Explanation opens after your attempt
Step 1
Concept
( (x-2)(x-5)=x-2 -7x+10 ). Exam tip: add the constants to get (-7).
Step 2
Why this answer is correct
The correct answer is C. (-7). ( (x-2)(x-5)=x-2 -7x+10 ). Exam tip: add the constants to get (-7).
Step 3
Exam Tip
( (x-2)(x-5)=x-2 -7x+10 ) है। परीक्षा में स्थिर पदों का योग (-7) लें।
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( (z+9)(z-9) ) का सही परिणाम चुनिए।
Choose the correct result of ( (z+9)(z-9) ).
#difference of squares
#z identity
#expansion
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A \(z^2+81\)
B \(z^2+18z+81\)
C \(z^2-18z+81\)
D \(z^2-81\)
Explanation opens after your attempt
Correct Answer
D. \(z^2-81\)
Step 1
Concept
( (z+9)(z-9)=z-2 -81 ). Exam tip: keep \(9^2=81\) in mind.
Step 2
Why this answer is correct
The correct answer is D. \(z^2-81\). ( (z+9)(z-9)=z-2 -81 ). Exam tip: keep \(9^2=81\) in mind.
Step 3
Exam Tip
( (z+9)(z-9)=z-2 -81 ) है। परीक्षा में \(9^2=81\) रखें।
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( (a+b+c)2 ) में (2ab) के साथ कौन-से अन्य दो गुणन पद आते हैं?
In ( (a+b+c)2 ), which two other product terms come with (2ab)?
#three term square
#abc identity
#product terms
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A (2ac) और (2bc)
B \(a^2\) और \(b^2\)
C (ab) और (bc)
D (3abc) और \(c^2\)
Explanation opens after your attempt
Correct Answer
A. (2ac) और (2bc)
Step 1
Concept
In ( (a+b+c)2 ), (2ab), (2bc), and (2ca) appear. Exam tip: remember the three pairwise product terms.
Step 2
Why this answer is correct
The correct answer is A. (2ac) और (2bc). In ( (a+b+c)2 ), (2ab), (2bc), and (2ca) appear. Exam tip: remember the three pairwise product terms.
Step 3
Exam Tip
( (a+b+c)2 ) में (2ab), (2bc), और (2ca) आते हैं। परीक्षा में तीन जोड़ी गुणन पद याद रखें।
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( (x+y+z)2 ) में वर्ग पद कौन-से हैं?
What are the square terms in ( (x+y+z)2 )?
#three term square
#square terms
#algebra
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A (xy), (yz), (zx)
B \(x^2\), \(y^2\), \(z^2\)
C (2xy), (2yz), (2zx)
D (x+y+z)
Explanation opens after your attempt
Correct Answer
B. \(x^2\), \(y^2\), \(z^2\)
Step 1
Concept
The square terms are \(x^2\), \(y^2\), \(z^2\). Exam tip: distinguish square terms and product terms.
Step 2
Why this answer is correct
The correct answer is B. \(x^2\), \(y^2\), \(z^2\). The square terms are \(x^2\), \(y^2\), \(z^2\). Exam tip: distinguish square terms and product terms.
Step 3
Exam Tip
वर्ग पद \(x^2\), \(y^2\), \(z^2\) हैं। परीक्षा में वर्ग पद और गुणन पद अलग पहचानें।
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( (a+b+c)2 ) का पूरा विस्तार कौन-सा है?
Which is the full expansion of ( (a+b+c)2 )?
#three term identity
#full expansion
#algebra
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A \(a^2+b^2+c^2+ab+bc+ca\)
B \(a^2+b^2+c^2+abc\)
C \(a^2+b^2+c^2+2ab+2bc+2ca\)
D \(a^2+b^2-c^2+2ab\)
Explanation opens after your attempt
Correct Answer
C. \(a^2+b^2+c^2+2ab+2bc+2ca\)
Step 1
Concept
The square of three terms has three square terms and three double product terms. Exam tip: write all terms with (2).
Step 2
Why this answer is correct
The correct answer is C. \(a^2+b^2+c^2+2ab+2bc+2ca\). The square of three terms has three square terms and three double product terms. Exam tip: write all terms with (2).
Step 3
Exam Tip
तीन पदों के वर्ग में तीन वर्ग पद और तीन दोहरे गुणन पद होते हैं। परीक्षा में सभी (2) वाले पद लिखें।
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( (x+2+y)2 ) में (2xy) क्यों आएगा?
Why will (2xy) appear in ( (x+2+y)2 )?
#three term square
#pair product
#2xy
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A क्योंकि (x) और (y) दोनों वर्ग पद हैं / Because (x) and (y) are both square terms
B क्योंकि (x) और (y) की जोड़ी का दोहरा गुणन आता है / Because the double product of the pair (x) and (y) appears
C क्योंकि (2) हमेशा हट जाता है / Because (2) always disappears
D क्योंकि कोई गुणन पद नहीं आता / Because no product term appears
Explanation opens after your attempt
Correct Answer
B. क्योंकि (x) और (y) की जोड़ी का दोहरा गुणन आता है / Because the double product of the pair (x) and (y) appears
Step 1
Concept
In the square of three terms, the double product of each pair appears. Exam tip: write terms by making pairs.
Step 2
Why this answer is correct
The correct answer is B. क्योंकि (x) और (y) की जोड़ी का दोहरा गुणन आता है / Because the double product of the pair (x) and (y) appears. In the square of three terms, the double product of each pair appears. Exam tip: write terms by making pairs.
Step 3
Exam Tip
तीन पदों के वर्ग में हर जोड़ी का दोहरा गुणन आता है। परीक्षा में जोड़ी बनाकर पद लिखें।
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\( a^2+2ab+b^2 \) को किस रूप में लिखा जा सकता है?
In which form can \( a^2+2ab+b^2 \) be written?
#factorisation
#square identity
#recognition
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A ( (a-b)2 )
B \(a^2-b^2\)
C ( (a+b)2 )
D \(a+b^2\)
Explanation opens after your attempt
Correct Answer
C. ( (a+b)2 )
Step 1
Concept
This is the expansion of ( (a+b)2 ). Exam tip: identify positive square from (+2ab).
Step 2
Why this answer is correct
The correct answer is C. ( (a+b)2 ). This is the expansion of ( (a+b)2 ). Exam tip: identify positive square from (+2ab).
Step 3
Exam Tip
यह ( (a+b)2 ) का विस्तार है। परीक्षा में (+2ab) देखकर धन वर्ग पहचानें।
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\( x^2-6x+9 \) को किस रूप में लिखा जाएगा?
In which form will \( x^2-6x+9 \) be written?
#factorisation
#perfect square
#x minus 3
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A ( (x+3)2 )
B \(x^2-9\)
C ( (x-6)2 )
D ( (x-3)2 )
Explanation opens after your attempt
Correct Answer
D. ( (x-3)2 )
Step 1
Concept
(x-2 -6x+9=x-2 -2\cdot x\cdot3+32 =(x-3)2 ). Exam tip: check the square root of the last term.
Step 2
Why this answer is correct
The correct answer is D. ( (x-3)2 ). (x-2 -6x+9=x-2 -2\cdot x\cdot3+32 =(x-3)2 ). Exam tip: check the square root of the last term.
Step 3
Exam Tip
(x-2 -6x+9=x-2 -2\cdot x\cdot3+32 =(x-3)2 )। परीक्षा में अंतिम पद का वर्गमूल देखें।
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\( y^2+12y+36 \) किसका वर्ग है?
\( y^2+12y+36 \) is the square of what?
#perfect square
#recognition
#y plus 6
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A ( (y+6)2 )
B ( (y-6)2 )
C ( (y+12)2 )
D \(y^2-36\)
Explanation opens after your attempt
Correct Answer
A. ( (y+6)2 )
Step 1
Concept
\(36=6^2\) and \(12y=2\cdot y\cdot6\). Exam tip: identify perfect square trinomials.
Step 2
Why this answer is correct
The correct answer is A. ( (y+6)2 ). \(36=6^2\) and \(12y=2\cdot y\cdot6\). Exam tip: identify perfect square trinomials.
Step 3
Exam Tip
\(36=6^2\) और \(12y=2\cdot y\cdot6\) है। परीक्षा में पूर्ण वर्ग त्रिपद पहचानें।
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\( 49-r^2 \) को गुणनखंडों में कैसे लिखेंगे?
How will you factorise \( 49-r^2 \)?
#factorisation
#difference of squares
#49 minus r square
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A ( (r+7)(r-7) )
B ( (7+r)(7-r) )
C ( (49+r)(49-r) )
D ( (7-r)2 )
Explanation opens after your attempt
Correct Answer
B. ( (7+r)(7-r) )
Step 1
Concept
(49-r-2 =72 -r-2 =(7+r)(7-r)). Exam tip: keep the larger square first.
Step 2
Why this answer is correct
The correct answer is B. ( (7+r)(7-r) ). (49-r-2 =72 -r-2 =(7+r)(7-r)). Exam tip: keep the larger square first.
Step 3
Exam Tip
(49-r-2 =72 -r-2 =(7+r)(7-r)) है। परीक्षा में बड़े वर्ग को पहले रखें।
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\( 25x^2-16 \) का सही गुणनखंडन क्या है?
What is the correct factorisation of \( 25x^2-16 \)?
#factorisation
#difference of squares
#25x square
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A ( (5x-4)2 )
B ( (25x-4)(x+4) )
C ( (5x+4)(5x-4) )
D ( (5x+4)2 )
Explanation opens after your attempt
Correct Answer
C. ( (5x+4)(5x-4) )
Step 1
Concept
(25x-2 -16=(5x)2 -42 =(5x+4)(5x-4)). Exam tip: identify both squares.
Step 2
Why this answer is correct
The correct answer is C. ( (5x+4)(5x-4) ). (25x-2 -16=(5x)2 -42 =(5x+4)(5x-4)). Exam tip: identify both squares.
Step 3
Exam Tip
(25x-2 -16=(5x)2 -42 =(5x+4)(5x-4))। परीक्षा में दोनों वर्ग पहचानें।
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( (a+1)2 ) और \(a^2+1\) में क्या अंतर है?
What is the difference between ( (a+1)2 ) and \(a^2+1\)?
#common mistake
#middle term
#square identity
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A दोनों हमेशा समान हैं / Both are always same
B ( (a+1)2 ) में मध्य पद (2a) भी होता है / ( (a+1)2 ) also has middle term (2a)
C \(a^2+1\) में (2a) होता है / \(a^2+1\) has (2a)
D दोनों में कोई वर्ग पद नहीं होता / Neither has square terms
Explanation opens after your attempt
Correct Answer
B. ( (a+1)2 ) में मध्य पद (2a) भी होता है / ( (a+1)2 ) also has middle term (2a)
Step 1
Concept
( (a+1)2 =a-2 +2a+1 ), so \(a^2+1\) is incomplete. Exam tip: do not omit the middle term.
Step 2
Why this answer is correct
The correct answer is B. ( (a+1)2 ) में मध्य पद (2a) भी होता है / ( (a+1)2 ) also has middle term (2a). ( (a+1)2 =a-2 +2a+1 ), so \(a^2+1\) is incomplete. Exam tip: do not omit the middle term.
Step 3
Exam Tip
( (a+1)2 =a-2 +2a+1 ), इसलिए \(a^2+1\) अधूरा है। परीक्षा में मध्य पद न छोड़ें।
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( (x-1)2 ) और \(x^2-1\) में सही अंतर कौन-सा है?
Which is the correct difference between ( (x-1)2 ) and \(x^2-1\)?
#common mistake
#x minus 1
#difference of squares
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A ( (x-1)2 =x-2 -2x+1 ), जबकि (x-2 -1=(x+1)(x-1))
B दोनों हमेशा समान हैं / Both are always same
C \(x^2-1=x^2-2x+1\)
D ( (x-1)2 =x-2 +2x+1 )
Explanation opens after your attempt
Correct Answer
A. ( (x-1)2 =x-2 -2x+1 ), जबकि (x-2 -1=(x+1)(x-1))
Step 1
Concept
The first is a perfect square and the second is difference of squares. Exam tip: keep bracket square and difference of squares separate.
Step 2
Why this answer is correct
The correct answer is A. ( (x-1)2 =x-2 -2x+1 ), जबकि (x-2 -1=(x+1)(x-1)). The first is a perfect square and the second is difference of squares. Exam tip: keep bracket square and difference of squares separate.
Step 3
Exam Tip
पहला पूर्ण वर्ग है और दूसरा वर्गों का अंतर है। परीक्षा में कोष्ठक और वर्गों का अंतर अलग रखें।
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( (2a+3)(2a-3) ) को सरल कीजिए।
Simplify ( (2a+3)(2a-3) ).
#simplification
#difference of squares
#2a plus 3
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A \(4a^2+9\)
B \(4a^2-9\)
C \(2a^2-9\)
D \(4a^2-12a+9\)
Explanation opens after your attempt
Correct Answer
B. \(4a^2-9\)
Step 1
Concept
This is ( (p+q)(p-q)=p-2 -q-2 ). Here take (p=2a) and (q=3).
Step 2
Why this answer is correct
The correct answer is B. \(4a^2-9\). This is ( (p+q)(p-q)=p-2 -q-2 ). Here take (p=2a) and (q=3).
Step 3
Exam Tip
यह ( (p+q)(p-q)=p-2 -q-2 ) है। यहाँ (p=2a) और (q=3) लें।
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( (6x+1)2 ) में (x) वाला पद क्या होगा?
What will be the term containing (x) in ( (6x+1)2 )?
#middle term
#6x plus 1
#square identity
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A (6x)
B (36x)
C (12x)
D (1x)
Explanation opens after your attempt
Step 1
Concept
The middle term is \(2\cdot6x\cdot1=12x\). Exam tip: use (2ab).
Step 2
Why this answer is correct
The correct answer is C. (12x). The middle term is \(2\cdot6x\cdot1=12x\). Exam tip: use (2ab).
Step 3
Exam Tip
मध्य पद \(2\cdot6x\cdot1=12x\) है। परीक्षा में (2ab) का प्रयोग करें।
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( (4p-1)2 ) का विस्तार क्या है?
What is the expansion of ( (4p-1)2 )?
#expansion
#4p minus 1
#identity
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A \(16p^2+8p+1\)
B \(16p^2-4p+1\)
C \(4p^2-8p+1\)
D \(16p^2-8p+1\)
Explanation opens after your attempt
Correct Answer
D. \(16p^2-8p+1\)
Step 1
Concept
( (4p-1)2 =16p-2 -8p+1 ). Exam tip: remember \(2\cdot4p\cdot1=8p\) and the negative sign.
Step 2
Why this answer is correct
The correct answer is D. \(16p^2-8p+1\). ( (4p-1)2 =16p-2 -8p+1 ). Exam tip: remember \(2\cdot4p\cdot1=8p\) and the negative sign.
Step 3
Exam Tip
( (4p-1)2 =16p-2 -8p+1 ) है। परीक्षा में \(2\cdot4p\cdot1=8p\) और ऋण चिह्न याद रखें।
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\( 104^2 \) को पहचान से निकालने के लिए सही रूप क्या है?
What is the correct form to find \( 104^2 \) using an identity?
#mental math
#104 square
#identity
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A ( (100+4)2 )
B ( (104-4)2 )
C ( (50+54)(50-54) )
D \(104^2-4^2\)
Explanation opens after your attempt
Correct Answer
A. ( (100+4)2 )
Step 1
Concept
(104=100+4), so ( (100+4)2 ) is suitable. Exam tip: choose a nearby round number.
Step 2
Why this answer is correct
The correct answer is A. ( (100+4)2 ). (104=100+4), so ( (100+4)2 ) is suitable. Exam tip: choose a nearby round number.
Step 3
Exam Tip
(104=100+4), इसलिए ( (100+4)2 ) उपयुक्त है। परीक्षा में नजदीकी पूर्ण संख्या चुनें।
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( (x+8)2 ) और ( (x-8)2 ) में किस पद का चिह्न बदलता है?
In ( (x+8)2 ) and ( (x-8)2 ), which term changes sign?
#sign change
#middle term
#plus minus square
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A वर्ग पद \(x^2\) / square term \(x^2\)
B मध्य पद (16x) / middle term (16x)
C स्थिर पद (64) / constant term (64)
D सभी पद / all terms
Explanation opens after your attempt
Correct Answer
B. मध्य पद (16x) / middle term (16x)
Step 1
Concept
In both, \(x^2\) and (64) remain same; only the sign of the middle term changes. Exam tip: compare signs.
Step 2
Why this answer is correct
The correct answer is B. मध्य पद (16x) / middle term (16x). In both, \(x^2\) and (64) remain same; only the sign of the middle term changes. Exam tip: compare signs.
Step 3
Exam Tip
दोनों में \(x^2\) और (64) समान रहते हैं, केवल मध्य पद का चिह्न बदलता है। परीक्षा में चिह्न तुलना करें।
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पहचानों का मुख्य उपयोग क्या है?
What is the main use of identities?
#algebraic identities
#use
#simplification
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A सिर्फ आकृतियाँ बनाने में / only drawing figures
B सिर्फ भिन्नों को पढ़ने में / only reading fractions
C व्यंजकों को जल्दी फैलाने और सरल करने में / expanding and simplifying expressions quickly
D केवल कोण नापने में / only measuring angles
Explanation opens after your attempt
Correct Answer
C. व्यंजकों को जल्दी फैलाने और सरल करने में / expanding and simplifying expressions quickly
Step 1
Concept
Algebraic identities make calculation shorter and systematic. Exam tip: identify the identity and apply it directly.
Step 2
Why this answer is correct
The correct answer is C. व्यंजकों को जल्दी फैलाने और सरल करने में / expanding and simplifying expressions quickly. Algebraic identities make calculation shorter and systematic. Exam tip: identify the identity and apply it directly.
Step 3
Exam Tip
बीजीय पहचानें गणना को छोटा और व्यवस्थित बनाती हैं। परीक्षा में पहचान पहचानकर सीधे लागू करें।
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( (a+b)2 ) का सही प्रसार कौन सा है?
What is the correct expansion of ( (a+b)2 )?
#algebraic identities
#square identity
#expansion
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A \(a^2+2ab+b^2\)
B \(a^2-2ab+b^2\)
C \(a^2+b^2\)
D \(a^2-ab+b^2\)
Explanation opens after your attempt
Correct Answer
A. \(a^2+2ab+b^2\)
Step 1
Concept
This is a standard identity. Exam tip: remember the middle term (2ab).
Step 2
Why this answer is correct
The correct answer is A. \(a^2+2ab+b^2\). This is a standard identity. Exam tip: remember the middle term (2ab).
Step 3
Exam Tip
यह मानक सर्वसमिका है। परीक्षा में बीच का पद (2ab) याद रखें।
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( (a-b)2 ) का सही प्रसार क्या है?
What is the correct expansion of ( (a-b)2 )?
#algebraic identities
#minus square
#expansion
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A \(a^2+b^2\)
B \(a^2-2ab+b^2\)
C \(a^2+2ab+b^2\)
D \(a^2-b^2\)
Explanation opens after your attempt
Correct Answer
B. \(a^2-2ab+b^2\)
Step 1
Concept
In the subtraction square identity the middle term is negative. Exam tip: focus on ( -2ab ).
Step 2
Why this answer is correct
The correct answer is B. \(a^2-2ab+b^2\). In the subtraction square identity the middle term is negative. Exam tip: focus on ( -2ab ).
Step 3
Exam Tip
घटाव वाली वर्ग सर्वसमिका में बीच का पद ऋणात्मक होता है। परीक्षा में ( -2ab ) पर ध्यान दें।
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( (x+5)2 ) का प्रसार चुनिए।
Choose the expansion of ( (x+5)2 ).
#square identity
#x plus number
#expansion
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A \(x^2+5x+25\)
B \(x^2+10x+5\)
C \(x^2+10x+25\)
D \(x^2-10x+25\)
Explanation opens after your attempt
Correct Answer
C. \(x^2+10x+25\)
Step 1
Concept
Using ( (a+b)2 =a-2 +2ab+b-2 ), \(2\cdot x\cdot5=10x\). Exam tip: multiply the middle term carefully.
Step 2
Why this answer is correct
The correct answer is C. \(x^2+10x+25\). Using ( (a+b)2 =a-2 +2ab+b-2 ), \(2\cdot x\cdot5=10x\). Exam tip: multiply the middle term carefully.
Step 3
Exam Tip
( (a+b)2 =a-2 +2ab+b-2 ) लगाने पर \(2\cdot x\cdot5=10x\) आता है। परीक्षा में बीच का गुणन ध्यान से करें।
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( (y-4)2 ) में बीच वाला पद क्या होगा?
What will be the middle term in ( (y-4)2 )?
#middle term
#minus square
#algebra
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A (8y)
B (4y)
C (-4y)
D (-8y)
Explanation opens after your attempt
Step 1
Concept
In ( (a-b)2 ), the middle term is (-2ab). Here it is \(-2\cdot y\cdot4=-8y\).
Step 2
Why this answer is correct
The correct answer is D. (-8y). In ( (a-b)2 ), the middle term is (-2ab). Here it is \(-2\cdot y\cdot4=-8y\).
Step 3
Exam Tip
( (a-b)2 ) में बीच का पद (-2ab) होता है। यहाँ \(-2\cdot y\cdot4=-8y\) है।
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( (p+q)(p-q) ) किसके बराबर है?
What is ( (p+q)(p-q) ) equal to?
#difference of squares
#product identity
#algebra
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A \(p^2-q^2\)
B \(p^2+q^2\)
C \(p^2+2pq+q^2\)
D \(p^2-2pq+q^2\)
Explanation opens after your attempt
Correct Answer
A. \(p^2-q^2\)
Step 1
Concept
This is the difference of squares identity. Exam tip: remember ( (a+b)(a-b)=a-2 -b-2 ).
Step 2
Why this answer is correct
The correct answer is A. \(p^2-q^2\). This is the difference of squares identity. Exam tip: remember ( (a+b)(a-b)=a-2 -b-2 ).
Step 3
Exam Tip
यह अंतर के वर्गों की सर्वसमिका है। परीक्षा में ( (a+b)(a-b)=a-2 -b-2 ) याद रखें।
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\( x^2-49 \) को गुणनखंड रूप में लिखिए।
Write \( x^2-49 \) in factor form.
#factorisation
#difference of squares
#x square
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A ( (x+7)2 )
B ( (x+7)(x-7) )
C ( (x-49)(x+1) )
D ( (x-7)2 )
Explanation opens after your attempt
Correct Answer
B. ( (x+7)(x-7) )
Step 1
Concept
Since \(49=7^2\), \(x^2-49=x^2-7^2\). Exam tip: identify squares first.
Step 2
Why this answer is correct
The correct answer is B. ( (x+7)(x-7) ). Since \(49=7^2\), \(x^2-49=x^2-7^2\). Exam tip: identify squares first.
Step 3
Exam Tip
\(49=7^2\), इसलिए \(x^2-49=x^2-7^2\) है। परीक्षा में वर्ग पहचानना जरूरी है।
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( (m+3)(m-3 ) ) का मान क्या होगा?
What will be the value of ( (m+3)(m-3 ) )?
#product identity
#m plus m minus
#difference squares
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A \(m^2+9\)
B \(m^2+6m+9\)
C \(m^2-9\)
D \(m^2-6m+9\)
Explanation opens after your attempt
Correct Answer
C. \(m^2-9\)
Step 1
Concept
This is the form ( (a+b)(a-b)=a-2 -b-2 ). Here \(3^2=9\).
Step 2
Why this answer is correct
The correct answer is C. \(m^2-9\). This is the form ( (a+b)(a-b)=a-2 -b-2 ). Here \(3^2=9\).
Step 3
Exam Tip
यह ( (a+b)(a-b)=a-2 -b-2 ) का रूप है। यहाँ \(3^2=9\) है।
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( (2x+1)2 ) का सही प्रसार कौन सा है?
Which is the correct expansion of ( (2x+1)2 )?
#square binomial
#2x plus 1
#expansion
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A \(4x^2+1\)
B \(2x^2+4x+1\)
C \(4x^2+2x+1\)
D \(4x^2+4x+1\)
Explanation opens after your attempt
Correct Answer
D. \(4x^2+4x+1\)
Step 1
Concept
Put (a=2x) and (b=1), so (2ab=4x). Exam tip: write ( (2x)2 =4x-2 ).
Step 2
Why this answer is correct
The correct answer is D. \(4x^2+4x+1\). Put (a=2x) and (b=1), so (2ab=4x). Exam tip: write ( (2x)2 =4x-2 ).
Step 3
Exam Tip
(a=2x) और (b=1) रखने पर (2ab=4x) मिलता है। परीक्षा में ( (2x)2 =4x-2 ) लिखें।
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( (3a-2)2 ) में (a) वाला पद कौन सा है?
Which is the (a)-term in ( (3a-2)2 )?
#middle term
#3a minus 2
#square identity
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A (-12a)
B (12a)
C (-6a)
D (6a)
Explanation opens after your attempt
Step 1
Concept
The middle term is \(-2\cdot3a\cdot2=-12a\). Exam tip: do not make the sign positive by mistake.
Step 2
Why this answer is correct
The correct answer is A. (-12a). The middle term is \(-2\cdot3a\cdot2=-12a\). Exam tip: do not make the sign positive by mistake.
Step 3
Exam Tip
बीच का पद \(-2\cdot3a\cdot2=-12a\) है। परीक्षा में चिन्ह को गलती से धनात्मक न करें।
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( (x+2)(x+5) ) का प्रसार क्या है?
What is the expansion of ( (x+2)(x+5) )?
#product of binomials
#x plus a
#x plus b
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A \(x^2+7\)
B \(x^2+7x+10\)
C \(x^2+10x+7\)
D \(x^2-7x+10\)
Explanation opens after your attempt
Correct Answer
B. \(x^2+7x+10\)
Step 1
Concept
( (x+a)(x+b)=x-2 +(a+b)x+ab ). Here (a+b=7) and (ab=10).
Step 2
Why this answer is correct
The correct answer is B. \(x^2+7x+10\). ( (x+a)(x+b)=x-2 +(a+b)x+ab ). Here (a+b=7) and (ab=10).
Step 3
Exam Tip
( (x+a)(x+b)=x-2 +(a+b)x+ab ) होता है। यहाँ (a+b=7) और (ab=10) है।
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( (t-3)(t+4) ) में स्थिर पद क्या है?
What is the constant term in ( (t-3)(t+4) )?
#constant term
#binomial product
#algebra
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A (12)
B (1)
C (-12)
D (-1)
Explanation opens after your attempt
Step 1
Concept
The constant term is ((-3)\cdot4=-12). Exam tip: product of numbers gives the constant term.
Step 2
Why this answer is correct
The correct answer is C. (-12). The constant term is ((-3)\cdot4=-12). Exam tip: product of numbers gives the constant term.
Step 3
Exam Tip
स्थिर पद ((-3)\cdot4=-12) है। परीक्षा में केवल संख्याओं का गुणन स्थिर पद देता है।
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( (a+b)2 +(a-b)2 ) किसके बराबर है?
What is ( (a+b)2 +(a-b)2 ) equal to?
#sum of squares identities
#algebraic simplification
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A \(2a^2+2b^2\)
B (4ab)
C \(a^2-b^2\)
D \(a^2+b^2+2ab\)
Explanation opens after your attempt
Correct Answer
A. \(2a^2+2b^2\)
Step 1
Concept
On adding, (+2ab) and (-2ab) cancel. Exam tip: add the remaining terms carefully.
Step 2
Why this answer is correct
The correct answer is A. \(2a^2+2b^2\). On adding, (+2ab) and (-2ab) cancel. Exam tip: add the remaining terms carefully.
Step 3
Exam Tip
जोड़ने पर (+2ab) और (-2ab) कट जाते हैं। परीक्षा में बचे हुए पदों को ध्यान से जोड़ें।
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\( 101^2 \) निकालने के लिए कौन सी सर्वसमिका सबसे उपयुक्त है?
Which identity is most suitable to find \( 101^2 \)?
#mental math
#101 square
#identity use
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A ( (a-b)2 )
B ( (a+b)2 )
C \( a^2-b^2 \)
D ( (x+a)(x+b) )
Explanation opens after your attempt
Correct Answer
B. ( (a+b)2 )
Step 1
Concept
Since (101=100+1), ( (a+b)2 ) is useful. Exam tip: choose a nearby easy number.
Step 2
Why this answer is correct
The correct answer is B. ( (a+b)2 ). Since (101=100+1), ( (a+b)2 ) is useful. Exam tip: choose a nearby easy number.
Step 3
Exam Tip
(101=100+1), इसलिए ( (a+b)2 ) उपयोगी है। परीक्षा में पास की आसान संख्या चुनें।
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\( 99^2 \) को ( (100-1)2 ) से निकालने पर मान क्या होगा?
Using ( (100-1)2 ), what is \( 99^2 \)?
#mental calculation
#99 square
#minus square
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A (9801)
B (9999)
C (10001)
D (9901)
Explanation opens after your attempt
Step 1
Concept
( (100-1)2 =10000-200+1=9801 ). Exam tip: subtract the middle term in minus identity.
Step 2
Why this answer is correct
The correct answer is A. (9801). ( (100-1)2 =10000-200+1=9801 ). Exam tip: subtract the middle term in minus identity.
Step 3
Exam Tip
( (100-1)2 =10000-200+1=9801 ) है। परीक्षा में घटाव वाली सर्वसमिका में बीच का पद घटाएँ।
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\( 52^2 \) को ( (50+2)2 ) से निकालने पर सही उत्तर कौन सा है?
Using ( (50+2)2 ), which is the correct value of \( 52^2 \)?
#52 square
#mental math
#algebraic identity
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A (2604)
B (2704)
C (2504)
D (2804)
Explanation opens after your attempt
Step 1
Concept
(2500+200+4=2704). Exam tip: do not forget the (2ab) term.
Step 2
Why this answer is correct
The correct answer is B. (2704). (2500+200+4=2704). Exam tip: do not forget the (2ab) term.
Step 3
Exam Tip
(2500+200+4=2704) मिलता है। परीक्षा में (2ab) वाला पद न भूलें।
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\( 48^2 \) को ( (50-2)2 ) से निकालने पर मान क्या है?
Using ( (50-2)2 ), what is \( 48^2 \)?
#48 square
#minus identity
#mental math
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A (2404)
B (2504)
C (2304)
D (2204)
Explanation opens after your attempt
Step 1
Concept
(2500-200+4=2304). Exam tip: the final \(b^2\) is always added.
Step 2
Why this answer is correct
The correct answer is C. (2304). (2500-200+4=2304). Exam tip: the final \(b^2\) is always added.
Step 3
Exam Tip
(2500-200+4=2304) होता है। परीक्षा में अंतिम \(b^2\) हमेशा जोड़ा जाता है।
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\( 63\times57 \) को जल्दी निकालने के लिए किस रूप में लिखना सही है?
To calculate \( 63\times57 \) quickly, which form is correct?
#product calculation
#difference of squares
#63 times 57
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A ( (60+3)(60+3) )
B ( (60-3)(60-3) )
C ( (63+57)2 )
D ( (60+3)(60-3) )
Explanation opens after your attempt
Correct Answer
D. ( (60+3)(60-3) )
Step 1
Concept
(63=60+3) and (57=60-3). Exam tip: identify ( (a+b)(a-b) ).
Step 2
Why this answer is correct
The correct answer is D. ( (60+3)(60-3) ). (63=60+3) and (57=60-3). Exam tip: identify ( (a+b)(a-b) ).
Step 3
Exam Tip
(63=60+3) और (57=60-3) है। परीक्षा में ( (a+b)(a-b) ) पहचानें।
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\( 75^2-25^2 \) का मान क्या होगा?
What is the value of \( 75^2-25^2 \)?
#difference of squares
#numerical identity
#75 square
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A (5000)
B (2500)
C (10000)
D (7500)
Explanation opens after your attempt
Step 1
Concept
(a-2 -b-2 =(a+b)(a-b)), so \(100\times50=5000\). Exam tip: use product form directly.
Step 2
Why this answer is correct
The correct answer is A. (5000). (a-2 -b-2 =(a+b)(a-b)), so \(100\times50=5000\). Exam tip: use product form directly.
Step 3
Exam Tip
(a-2 -b-2 =(a+b)(a-b)), इसलिए \(100\times50=5000\) है। परीक्षा में सीधे गुणन रूप लगाएँ।
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( (x+6)2 =x-2 +__+36 ) में रिक्त स्थान क्या होगा?
In ( (x+6)2 =x-2 +__+36 ), what will fill the blank?
#fill blank
#square identity
#algebra
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A (6x)
B (12x)
C (18x)
D (36x)
Explanation opens after your attempt
Step 1
Concept
The middle term is \(2\cdot x\cdot6=12x\). Exam tip: from \(b^2=36\), identify (b=6).
Step 2
Why this answer is correct
The correct answer is B. (12x). The middle term is \(2\cdot x\cdot6=12x\). Exam tip: from \(b^2=36\), identify (b=6).
Step 3
Exam Tip
बीच का पद \(2\cdot x\cdot6=12x\) है। परीक्षा में \(b^2=36\) देखकर (b=6) पहचानें।
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( (z-8)2 =z-2 -16z+__ ) में रिक्त स्थान क्या है?
In ( (z-8)2 =z-2 -16z+__ ), what is the blank?
#fill blank
#minus square
#last term
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A (8)
B (16)
C (64)
D (32)
Explanation opens after your attempt
Step 1
Concept
The last term is \(8^2=64\). Exam tip: the last term in square identity is always positive.
Step 2
Why this answer is correct
The correct answer is C. (64). The last term is \(8^2=64\). Exam tip: the last term in square identity is always positive.
Step 3
Exam Tip
अंतिम पद \(8^2=64\) है। परीक्षा में वर्ग सर्वसमिका में अंतिम पद हमेशा धनात्मक होता है।
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( (r+s)2 ) में \(r^2\) और \(s^2\) के अलावा कौन सा पद आता है?
Besides \(r^2\) and \(s^2\), which term appears in ( (r+s)2 )?
#middle term
#plus square
#common mistake
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A (-2rs)
B (rs)
C (-rs)
D (2rs)
Explanation opens after your attempt
Step 1
Concept
In the plus square, the middle term is (2rs). Exam tip: do not write ( (r+s)2 ) as only \(r^2+s^2\).
Step 2
Why this answer is correct
The correct answer is D. (2rs). In the plus square, the middle term is (2rs). Exam tip: do not write ( (r+s)2 ) as only \(r^2+s^2\).
Step 3
Exam Tip
जोड़ वाले वर्ग में बीच का पद (2rs) होता है। परीक्षा में ( (r+s)2 ) को केवल \(r^2+s^2\) न लिखें।
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( (2p+3q)2 ) का (pq) वाला पद क्या होगा?
What is the (pq)-term in ( (2p+3q)2 )?
#middle term
#coefficients
#square identity
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A (12pq)
B (6pq)
C (9pq)
D (4pq)
Explanation opens after your attempt
Step 1
Concept
The middle term is \(2\cdot2p\cdot3q=12pq\). Exam tip: multiply the coefficients too.
Step 2
Why this answer is correct
The correct answer is A. (12pq). The middle term is \(2\cdot2p\cdot3q=12pq\). Exam tip: multiply the coefficients too.
Step 3
Exam Tip
बीच का पद \(2\cdot2p\cdot3q=12pq\) है। परीक्षा में गुणांकों को भी गुणा करें।
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( (4x-1)2 ) का स्थिर पद क्या है?
What is the constant term of ( (4x-1)2 )?
#constant term
#minus square
#4x minus 1
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A (-1)
B (1)
C (-2)
D (8)
Explanation opens after your attempt
Step 1
Concept
The last term is ((-1)2 =1). Exam tip: the square of a number is positive.
Step 2
Why this answer is correct
The correct answer is B. (1). The last term is ((-1)2 =1). Exam tip: the square of a number is positive.
Step 3
Exam Tip
अंतिम पद ((-1)2 =1) होता है। परीक्षा में किसी संख्या का वर्ग धनात्मक होता है।
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\( x^2+14x+49 \) किसका वर्ग है?
\( x^2+14x+49 \) is the square of what?
#perfect square
#trinomial
#x plus 7
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A ( (x+14)2 )
B ( (x-7)2 )
C ( (x+7)2 )
D ( (x+49)2 )
Explanation opens after your attempt
Correct Answer
C. ( (x+7)2 )
Step 1
Concept
\(49=7^2\) and \(14x=2\cdot x\cdot7\). Exam tip: identify the square from first and last terms.
Step 2
Why this answer is correct
The correct answer is C. ( (x+7)2 ). \(49=7^2\) and \(14x=2\cdot x\cdot7\). Exam tip: identify the square from first and last terms.
Step 3
Exam Tip
\(49=7^2\) और \(14x=2\cdot x\cdot7\) है। परीक्षा में पहला और अंतिम पद देखकर वर्ग पहचानें।
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\( y^2-10y+25 \) किसका वर्ग है?
\( y^2-10y+25 \) is the square of what?
#perfect square
#minus square
#y minus 5
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A ( (y+5)2 )
B ( (y+10)2 )
C ( (y-10)2 )
D ( (y-5)2 )
Explanation opens after your attempt
Correct Answer
D. ( (y-5)2 )
Step 1
Concept
\(25=5^2\) and the middle term is (-10y). Therefore it is ( (y-5)2 ).
Step 2
Why this answer is correct
The correct answer is D. ( (y-5)2 ). \(25=5^2\) and the middle term is (-10y). Therefore it is ( (y-5)2 ).
Step 3
Exam Tip
\(25=5^2\) और बीच का पद (-10y) है। इसलिए यह ( (y-5)2 ) है।
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\( a^2-b^2 \) का गुणनखंड रूप कौन सा है?
What is the factor form of \( a^2-b^2 \)?
#factor form
#difference of squares
#identity
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A ( (a+b)(a-b) )
B ( (a-b)2 )
C ( (a+b)2 )
D \( a^2+2ab+b^2 \)
Explanation opens after your attempt
Correct Answer
A. ( (a+b)(a-b) )
Step 1
Concept
The factor form of difference of squares is ( (a+b)(a-b) ). Exam tip: recognize it quickly.
Step 2
Why this answer is correct
The correct answer is A. ( (a+b)(a-b) ). The factor form of difference of squares is ( (a+b)(a-b) ). Exam tip: recognize it quickly.
Step 3
Exam Tip
दो वर्गों के अंतर का गुणनखंड ( (a+b)(a-b) ) होता है। परीक्षा में इसे तुरंत पहचानें।
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( (x+9)(x-9) ) में कौन सा पद नहीं आएगा?
Which term will not appear in ( (x+9)(x-9) )?
#middle term cancellation
#difference of squares
#x plus 9
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A \(x^2\)
B (18x)
C (-81)
D \(x^2-81\)
Explanation opens after your attempt
Step 1
Concept
( (x+9)(x-9)=x-2 -81 ), so the middle term cancels. Exam tip: opposite sign terms add to zero.
Step 2
Why this answer is correct
The correct answer is B. (18x). ( (x+9)(x-9)=x-2 -81 ), so the middle term cancels. Exam tip: opposite sign terms add to zero.
Step 3
Exam Tip
( (x+9)(x-9)=x-2 -81 ) होता है, बीच का पद कट जाता है। परीक्षा में विपरीत चिन्ह वाले पदों का योग शून्य देखें।
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( (x+1)(x+9) ) में (x) का गुणांक क्या है?
What is the coefficient of (x) in ( (x+1)(x+9) )?
#coefficient
#x plus a
#x plus b
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A (9)
B (10)
C (1)
D (90)
Explanation opens after your attempt
Step 1
Concept
In ( (x+a)(x+b) ), the coefficient of (x) is (a+b). Here (1+9=10).
Step 2
Why this answer is correct
The correct answer is B. (10). In ( (x+a)(x+b) ), the coefficient of (x) is (a+b). Here (1+9=10).
Step 3
Exam Tip
( (x+a)(x+b) ) में (x) का गुणांक (a+b) होता है। यहाँ (1+9=10) है।
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( (x-2)(x-7) ) में स्थिर पद क्या होगा?
What will be the constant term in ( (x-2)(x-7) )?
#constant term
#negative factors
#binomial product
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A (14)
B (-14)
C (-9)
D (9)
Explanation opens after your attempt
Step 1
Concept
The constant term is ((-2)(-7)=14). Exam tip: product of two negative numbers is positive.
Step 2
Why this answer is correct
The correct answer is A. (14). The constant term is ((-2)(-7)=14). Exam tip: product of two negative numbers is positive.
Step 3
Exam Tip
स्थिर पद ((-2)(-7)=14) है। परीक्षा में दो ऋणात्मक संख्याओं का गुणन धनात्मक होता है।
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( (x-4)(x+6) ) में (x) का गुणांक क्या है?
What is the coefficient of (x) in ( (x-4)(x+6) )?
#coefficient
#binomial product
#x term
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A (-24)
B (2)
C (-2)
D (10)
Explanation opens after your attempt
Step 1
Concept
The coefficient of (x) is (-4+6=2). Exam tip: take the algebraic sum of the numbers.
Step 2
Why this answer is correct
The correct answer is B. (2). The coefficient of (x) is (-4+6=2). Exam tip: take the algebraic sum of the numbers.
Step 3
Exam Tip
(x) का गुणांक (-4+6=2) है। परीक्षा में संख्याओं का बीजगणितीय योग लें।
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( (2x+5)(2x-5) ) का मान क्या है?
What is the value of ( (2x+5)(2x-5) )?
#difference of squares
#2x plus 5
#product
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A \(4x^2+25\)
B \(2x^2-25\)
C \(4x^2-25\)
D \(4x^2-10x+25\)
Explanation opens after your attempt
Correct Answer
C. \(4x^2-25\)
Step 1
Concept
This is \(a^2-b^2\), where (a=2x) and (b=5). So the answer is \(4x^2-25\).
Step 2
Why this answer is correct
The correct answer is C. \(4x^2-25\). This is \(a^2-b^2\), where (a=2x) and (b=5). So the answer is \(4x^2-25\).
Step 3
Exam Tip
यह \(a^2-b^2\) है जहाँ (a=2x) और (b=5) है। इसलिए उत्तर \(4x^2-25\) है।
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( (5m+2n)2 ) में पहला पद क्या होगा?
What will be the first term in ( (5m+2n)2 )?
#first term
#coefficient square
#binomial square
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A \(5m^2\)
B (10mn)
C (25m)
D \(25m^2\)
Explanation opens after your attempt
Correct Answer
D. \(25m^2\)
Step 1
Concept
The first term is ( (5m)2 =25m-2 ). Exam tip: do not forget to square the coefficient.
Step 2
Why this answer is correct
The correct answer is D. \(25m^2\). The first term is ( (5m)2 =25m-2 ). Exam tip: do not forget to square the coefficient.
Step 3
Exam Tip
पहला पद ( (5m)2 =25m-2 ) होता है। परीक्षा में गुणांक का वर्ग लेना न भूलें।
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( (u-v)2 ) में अंतिम पद कौन सा होता है?
What is the last term in ( (u-v)2 )?
#last term
#minus square
#identity basics
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A \(v^2\)
B \(-v^2\)
C (-2uv)
D (uv)
Explanation opens after your attempt
Correct Answer
A. \(v^2\)
Step 1
Concept
In the square identity, the last term is \(v^2\) and remains positive. Exam tip: the minus sign affects the middle term.
Step 2
Why this answer is correct
The correct answer is A. \(v^2\). In the square identity, the last term is \(v^2\) and remains positive. Exam tip: the minus sign affects the middle term.
Step 3
Exam Tip
वर्ग सर्वसमिका में अंतिम पद \(v^2\) होता है और धनात्मक रहता है। परीक्षा में ऋण चिन्ह केवल बीच के पद पर आता है।
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( (7+3)2 ) को सर्वसमिका से निकालने पर कौन सा रूप सही है?
Using identity, which form is correct for ( (7+3)2 )?
#numeric identity
#plus square
#7 plus 3
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A \(7^2-2\cdot7\cdot3+3^2\)
B \(7^2+2\cdot7\cdot3+3^2\)
C \(7^2-3^2\)
D \(7^2+3^2\)
Explanation opens after your attempt
Correct Answer
B. \(7^2+2\cdot7\cdot3+3^2\)
Step 1
Concept
In the plus square identity, (+2ab) appears. Exam tip: keep ( (a+b)2 ) and ( (a-b)2 ) separate.
Step 2
Why this answer is correct
The correct answer is B. \(7^2+2\cdot7\cdot3+3^2\). In the plus square identity, (+2ab) appears. Exam tip: keep ( (a+b)2 ) and ( (a-b)2 ) separate.
Step 3
Exam Tip
जोड़ वाली वर्ग सर्वसमिका में (+2ab) आता है। परीक्षा में ( (a+b)2 ) और ( (a-b)2 ) अलग रखें।
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( (10-3)2 ) के लिए कौन सा विस्तार सही है?
Which expansion is correct for ( (10-3)2 )?
#numeric identity
#minus square
#10 minus 3
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A \(10^2+2\cdot10\cdot3+3^2\)
B \(10^2-3^2\)
C \(10^2-2\cdot10\cdot3+3^2\)
D \(10^2+3^2\)
Explanation opens after your attempt
Correct Answer
C. \(10^2-2\cdot10\cdot3+3^2\)
Step 1
Concept
In the minus square identity, the middle term is subtracted. Exam tip: the final \(3^2\) is still added.
Step 2
Why this answer is correct
The correct answer is C. \(10^2-2\cdot10\cdot3+3^2\). In the minus square identity, the middle term is subtracted. Exam tip: the final \(3^2\) is still added.
Step 3
Exam Tip
घटाव वाली वर्ग सर्वसमिका में बीच का पद घटता है। परीक्षा में अंतिम \(3^2\) फिर भी जोड़ा जाता है।
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\( 104\times96 \) को किस सर्वसमिका से जल्दी निकाला जा सकता है?
Which identity can quickly calculate \( 104\times96 \)?
#mental calculation
#difference of squares
#104 times 96
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A ( (a+b)2 )
B ( (a-b)2 )
C ( (a+b)(a-b)=a-2 -b-2 )
D ( (x+a)(x+b) )
Explanation opens after your attempt
Correct Answer
C. ( (a+b)(a-b)=a-2 -b-2 )
Step 1
Concept
(104=100+4) and (96=100-4). So the difference of squares identity is useful.
Step 2
Why this answer is correct
The correct answer is C. ( (a+b)(a-b)=a-2 -b-2 ). (104=100+4) and (96=100-4). So the difference of squares identity is useful.
Step 3
Exam Tip
(104=100+4) और (96=100-4) है। इसलिए अंतर के वर्गों की सर्वसमिका उपयोगी है।
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( (3x+4)2 ) में \(x^2\) का गुणांक क्या है?
What is the coefficient of \(x^2\) in ( (3x+4)2 )?
#coefficient
#x square
#3x plus 4
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A (3)
B (6)
C (9)
D (12)
Explanation opens after your attempt
Step 1
Concept
( (3x)2 =9x-2 ). Exam tip: square the whole (3x).
Step 2
Why this answer is correct
The correct answer is C. (9). ( (3x)2 =9x-2 ). Exam tip: square the whole (3x).
Step 3
Exam Tip
( (3x)2 =9x-2 ) है। परीक्षा में (3x) का पूरा वर्ग लें।
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( (a+2b)2 ) का प्रसार कौन सा है?
Which is the expansion of ( (a+2b)2 )?
#a plus 2b
#square expansion
#algebraic identity
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A \(a^2+4ab+4b^2\)
B \(a^2+2ab+2b^2\)
C \(a^2+4b^2\)
D \(a^2-4ab+4b^2\)
Explanation opens after your attempt
Correct Answer
A. \(a^2+4ab+4b^2\)
Step 1
Concept
Here the (2ab) term is \(2\cdot a\cdot2b=4ab\). Exam tip: calculate ( (2b)2 =4b-2 ).
Step 2
Why this answer is correct
The correct answer is A. \(a^2+4ab+4b^2\). Here the (2ab) term is \(2\cdot a\cdot2b=4ab\). Exam tip: calculate ( (2b)2 =4b-2 ).
Step 3
Exam Tip
यहाँ (2ab) वाला पद \(2\cdot a\cdot2b=4ab\) है। परीक्षा में ( (2b)2 =4b-2 ) करें।
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( (p-5q)2 ) का सही प्रसार चुनिए।
Choose the correct expansion of ( (p-5q)2 ).
#p minus 5q
#square expansion
#minus identity
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A \(p^2-5pq+25q^2\)
B \(p^2-10pq+25q^2\)
C \(p^2+10pq+25q^2\)
D \(p^2-25q^2\)
Explanation opens after your attempt
Correct Answer
B. \(p^2-10pq+25q^2\)
Step 1
Concept
The middle term is \(-2\cdot p\cdot5q=-10pq\). Exam tip: write the square of (5q) as \(25q^2\).
Step 2
Why this answer is correct
The correct answer is B. \(p^2-10pq+25q^2\). The middle term is \(-2\cdot p\cdot5q=-10pq\). Exam tip: write the square of (5q) as \(25q^2\).
Step 3
Exam Tip
बीच का पद \(-2\cdot p\cdot5q=-10pq\) है। परीक्षा में (5q) का वर्ग \(25q^2\) लिखें।
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( (x+4)2 -(x-4)2 ) का सरल रूप क्या है?
What is the simplified form of ( (x+4)2 -(x-4)2 )?
#identity simplification
#4ab
#x plus minus 4
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A (8x)
B (4x)
C (16x)
D (32x)
Explanation opens after your attempt
Step 1
Concept
( (a+b)2 -(a-b)2 =4ab ). Here (a=x), (b=4), so it is (16x).
Step 2
Why this answer is correct
The correct answer is C. (16x). ( (a+b)2 -(a-b)2 =4ab ). Here (a=x), (b=4), so it is (16x).
Step 3
Exam Tip
( (a+b)2 -(a-b)2 =4ab ) है। यहाँ (a=x), (b=4), इसलिए (16x) है।
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( (x+4)2 +(x-4)2 ) का सरल रूप क्या है?
What is the simplified form of ( (x+4)2 +(x-4)2 )?
#sum identity
#plus minus square
#simplification
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A \(2x^2+32\)
B \(2x^2+16\)
C \(x^2+32\)
D \(4x^2+16\)
Explanation opens after your attempt
Correct Answer
A. \(2x^2+32\)
Step 1
Concept
( (a+b)2 +(a-b)2 =2a-2 +2b-2 ). Here it gives \(2x^2+2\cdot16=2x^2+32\).
Step 2
Why this answer is correct
The correct answer is A. \(2x^2+32\). ( (a+b)2 +(a-b)2 =2a-2 +2b-2 ). Here it gives \(2x^2+2\cdot16=2x^2+32\).
Step 3
Exam Tip
( (a+b)2 +(a-b)2 =2a-2 +2b-2 ) है। यहाँ \(2x^2+2\cdot16=2x^2+32\) मिलेगा।
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\( 37^2-13^2 \) का मान क्या है?
What is the value of \( 37^2-13^2 \)?
#numeric difference squares
#37 square
#13 square
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A (600)
B (1200)
C (900)
D (500)
Explanation opens after your attempt
Step 1
Concept
(a-2 -b-2 =(a+b)(a-b)), so \(50\times24=1200\). Exam tip: find (a+b) and (a-b) directly.
Step 2
Why this answer is correct
The correct answer is B. (1200). (a-2 -b-2 =(a+b)(a-b)), so \(50\times24=1200\). Exam tip: find (a+b) and (a-b) directly.
Step 3
Exam Tip
(a-2 -b-2 =(a+b)(a-b)), इसलिए \(50\times24=1200\) है। परीक्षा में सीधे (a+b) और (a-b) निकालें।
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\( 1002^2 \) निकालने के लिए (1002) को किस रूप में लिखना अच्छा है?
To calculate \(1002^2\), how is it good to write (1002)?
#large square
#1002 square
#identity method
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A (1000-2)
B (100+2)
C (1000+2)
D (10+2)
Explanation opens after your attempt
Correct Answer
C. (1000+2)
Step 1
Concept
(1002=1000+2), so ( (a+b)2 ) becomes easy. Exam tip: choose a nearby round number.
Step 2
Why this answer is correct
The correct answer is C. (1000+2). (1002=1000+2), so ( (a+b)2 ) becomes easy. Exam tip: choose a nearby round number.
Step 3
Exam Tip
(1002=1000+2) है, इसलिए ( (a+b)2 ) आसान बनेगा। परीक्षा में पास की गोल संख्या चुनें।
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( (m+n)2 ) और \(m^2+n^2\) में क्या अंतर है?
What is the difference between ( (m+n)2 ) and \(m^2+n^2\)?
#common error
#square identity
#extra term
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A कोई अंतर नहीं है / There is no difference
B (2mn)
C (-2mn)
D (mn)
Explanation opens after your attempt
Step 1
Concept
( (m+n)2 =m-2 +2mn+n-2 ), so the extra term is (2mn). Exam tip: remember this common mistake.
Step 2
Why this answer is correct
The correct answer is B. (2mn). ( (m+n)2 =m-2 +2mn+n-2 ), so the extra term is (2mn). Exam tip: remember this common mistake.
Step 3
Exam Tip
( (m+n)2 =m-2 +2mn+n-2 ), इसलिए अतिरिक्त पद (2mn) है। परीक्षा में यह सामान्य गलती याद रखें।
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( (m-n)2 ) और \(m^2+n^2\) में कौन सा अतिरिक्त पद होता है?
Which extra term is present in ( (m-n)2 ) compared with \(m^2+n^2\)?
#minus square
#extra term
#common error
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A (2mn)
B (-2mn)
C (mn)
D (-mn)
Explanation opens after your attempt
Step 1
Concept
( (m-n)2 =m-2 -2mn+n-2 ). Exam tip: write (-2mn) in the minus square identity.
Step 2
Why this answer is correct
The correct answer is B. (-2mn). ( (m-n)2 =m-2 -2mn+n-2 ). Exam tip: write (-2mn) in the minus square identity.
Step 3
Exam Tip
( (m-n)2 =m-2 -2mn+n-2 ) है। परीक्षा में घटाव वाली सर्वसमिका में (-2mn) लिखें।
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( (x+3)2 =x-2 +6x+9 ) में (9) कहाँ से आया?
In ( (x+3)2 =x-2 +6x+9 ), where did (9) come from?
#last term
#x plus 3
#square identity
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A \(x^2\) से / From \(x^2\)
B \(2\cdot x\cdot3\) से / From \(2\cdot x\cdot3\)
C \(3^2\) से / From \(3^2\)
D (x+3) से / From (x+3)
Explanation opens after your attempt
Correct Answer
C. \(3^2\) से / From \(3^2\)
Step 1
Concept
The last term comes from the square of the second term. Exam tip: remember \(3^2=9\).
Step 2
Why this answer is correct
The correct answer is C. \(3^2\) से / From \(3^2\). The last term comes from the square of the second term. Exam tip: remember \(3^2=9\).
Step 3
Exam Tip
अंतिम पद दूसरे पद के वर्ग से आता है। परीक्षा में \(3^2=9\) याद रखें।
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( (2a-b)2 ) में बीच वाला पद क्या है?
What is the middle term in ( (2a-b)2 )?
#middle term
#2a minus b
#square identity
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A (2ab)
B (-2ab)
C (4ab)
D (-4ab)
Explanation opens after your attempt
Step 1
Concept
The middle term is \(-2\cdot2a\cdot b=-4ab\). Exam tip: include the coefficient of the first term.
Step 2
Why this answer is correct
The correct answer is D. (-4ab). The middle term is \(-2\cdot2a\cdot b=-4ab\). Exam tip: include the coefficient of the first term.
Step 3
Exam Tip
बीच का पद \(-2\cdot2a\cdot b=-4ab\) है। परीक्षा में पहले पद का गुणांक शामिल करें।
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( (x+8)(x-8) ) का सरल रूप क्या होगा?
What will be the simplified form of ( (x+8)(x-8) )?
#difference of squares
#x plus 8
#x minus 8
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A \(x^2+64\)
B \(x^2-16x+64\)
C \(x^2-64\)
D \(x^2+16x+64\)
Explanation opens after your attempt
Correct Answer
C. \(x^2-64\)
Step 1
Concept
This is \(x^2-8^2\). Exam tip: treat products with opposite signs as \(a^2-b^2\).
Step 2
Why this answer is correct
The correct answer is C. \(x^2-64\). This is \(x^2-8^2\). Exam tip: treat products with opposite signs as \(a^2-b^2\).
Step 3
Exam Tip
यह \(x^2-8^2\) है। परीक्षा में विपरीत चिन्हों वाले गुणनफल को \(a^2-b^2\) मानें।
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( (x+10)2 ) में बीच वाला पद क्या होगा?
What will be the middle term in ( (x+10)2 )?
#middle term
#square identity
#x plus 10
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A (10x)
B (20x)
C (100x)
D \(x^2\)
Explanation opens after your attempt
Step 1
Concept
The middle term is \(2\cdot x\cdot10=20x\). Exam tip: always write the (2ab) term.
Step 2
Why this answer is correct
The correct answer is B. (20x). The middle term is \(2\cdot x\cdot10=20x\). Exam tip: always write the (2ab) term.
Step 3
Exam Tip
बीच का पद \(2\cdot x\cdot10=20x\) होता है। परीक्षा में (2ab) वाला पद जरूर लिखें।
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( (3x+2)(3x-2) ) का सरल रूप क्या है?
What is the simplified form of ( (3x+2)(3x-2) )?
#difference of squares
#3x plus 2
#algebraic identity
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A \(9x^2-4\)
B \(9x^2+4\)
C \(3x^2-4\)
D \(9x^2-12x+4\)
Explanation opens after your attempt
Correct Answer
A. \(9x^2-4\)
Step 1
Concept
This is the form \(a^2-b^2\), where (a=3x) and (b=2). Exam tip: calculate ((3x)2 =9x-2 ).
Step 2
Why this answer is correct
The correct answer is A. \(9x^2-4\). This is the form \(a^2-b^2\), where (a=3x) and (b=2). Exam tip: calculate ((3x)2 =9x-2 ).
Step 3
Exam Tip
यह \(a^2-b^2\) का रूप है जहाँ (a=3x) और (b=2) है। परीक्षा में ((3x)2 =9x-2 ) करें।
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( (x+5)2 ) का विस्तार क्या है?
What is the expansion of ( (x+5)2 )?
#algebraic identities
#square expansion
#binomial
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A \(x^2+10x+25\)
B \(x^2+5x+25\)
C \(x^2+25\)
D \(x^2-10x+25\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+10x+25\)
Step 1
Concept
Using identity ( (a+b)2 =a-2 +2ab+b-2 ) gives the answer. Exam tip: do not forget the middle term (2ab).
Step 2
Why this answer is correct
The correct answer is A. \(x^2+10x+25\). Using identity ( (a+b)2 =a-2 +2ab+b-2 ) gives the answer. Exam tip: do not forget the middle term (2ab).
Step 3
Exam Tip
पहचान ( (a+b)2 =a-2 +2ab+b-2 ) लगाने पर उत्तर मिलता है। परीक्षा में बीच का पद (2ab) भूलें नहीं।
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पहचान ( (a-b)2 ) का सही विस्तार कौन-सा है?
Which is the correct expansion of the identity ( (a-b)2 )?
#algebraic identities
#minus square
#expansion
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A \(a^2+2ab+b^2\) / योग का वर्ग
B \(a^2-b^2\) / वर्गों का अंतर
C \(a^2-2ab+b^2\) / सही विस्तार
D \(a^2-ab+b^2\) / मध्य पद अधूरा
Explanation opens after your attempt
Correct Answer
C. \(a^2-2ab+b^2\) / सही विस्तार
Step 1
Concept
In ( (a-b)2 ), the middle term is (-2ab). Exam tip: check the negative sign carefully.
Step 2
Why this answer is correct
The correct answer is C. \(a^2-2ab+b^2\) / सही विस्तार. In ( (a-b)2 ), the middle term is (-2ab). Exam tip: check the negative sign carefully.
Step 3
Exam Tip
( (a-b)2 ) में मध्य पद (-2ab) होता है। परीक्षा में ऋण चिह्न ध्यान से देखें।
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( (y-4)2 ) का सही विस्तार चुनिए।
Choose the correct expansion of ( (y-4)2 ).
#algebraic identities
#minus square
#expansion
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A \(y^2-4y+16\)
B \(y^2-8y+16\)
C \(y^2+8y+16\)
D \(y^2-16\)
Explanation opens after your attempt
Correct Answer
B. \(y^2-8y+16\)
Step 1
Concept
By ( (a-b)2 =a-2 -2ab+b-2 ) the middle term is negative. Exam tip: note that \(2\times y\times4=8y\).
Step 2
Why this answer is correct
The correct answer is B. \(y^2-8y+16\). By ( (a-b)2 =a-2 -2ab+b-2 ) the middle term is negative. Exam tip: note that \(2\times y\times4=8y\).
Step 3
Exam Tip
( (a-b)2 =a-2 -2ab+b-2 ) से बीच का पद ऋणात्मक होता है। परीक्षा में \(2\times y\times4=8y\) ध्यान रखें।
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\(36-x^2\) का सही गुणनखंडन क्या है?
What is the correct factorisation of \(36-x^2\)?
#difference of squares
#factorisation
#36 minus x square
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A ( (x+6)(x-6) ) / क्रम उल्टा
B ( (6+x)(6-x) ) / सही गुणनखंड
C ( (36+x)(36-x) ) / वर्गमूल गलत
D ( (6-x)2 ) / पूर्ण वर्ग नहीं
Explanation opens after your attempt
Correct Answer
B. ( (6+x)(6-x) ) / सही गुणनखंड
Step 1
Concept
\(36-x^2=6^2-x^2\). Exam tip: identify both square roots in difference of squares.
Step 2
Why this answer is correct
The correct answer is B. ( (6+x)(6-x) ) / सही गुणनखंड. \(36-x^2=6^2-x^2\). Exam tip: identify both square roots in difference of squares.
Step 3
Exam Tip
\(36-x^2=6^2-x^2\) है। परीक्षा में वर्गों के अंतर में दोनों वर्गमूल पहचानें।
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( (p+7)(p-7) ) किसके बराबर है?
What is ( (p+7)(p-7) ) equal to?
#difference of squares
#product identity
#algebra
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A \(p^2+49\)
B \(p^2+14p+49\)
C \(p^2-49\)
D \(p^2-14p+49\)
Explanation opens after your attempt
Correct Answer
C. \(p^2-49\)
Step 1
Concept
This is the form ( (a+b)(a-b)=a-2 -b-2 ). Exam tip: identify difference of squares in opposite-sign factors.
Step 2
Why this answer is correct
The correct answer is C. \(p^2-49\). This is the form ( (a+b)(a-b)=a-2 -b-2 ). Exam tip: identify difference of squares in opposite-sign factors.
Step 3
Exam Tip
यह ( (a+b)(a-b)=a-2 -b-2 ) का रूप है। परीक्षा में विपरीत चिन्ह वाले पदों में अंतर वर्ग पहचानें।
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( (x+4)(x+6) ) में (x) का गुणांक क्या होगा?
What will be the coefficient of (x) in ( (x+4)(x+6) )?
#product identity
#coefficient
#x plus numbers
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A (10) / स्थिर पदों का योग
B (24) / स्थिर पदों का गुणन
C (4) / पहला स्थिर पद
D (6) / दूसरा स्थिर पद
Explanation opens after your attempt
Correct Answer
A. (10) / स्थिर पदों का योग
Step 1
Concept
( (x+4)(x+6)=x-2 +10x+24 ). Exam tip: the coefficient of (x) comes from the sum of constants.
Step 2
Why this answer is correct
The correct answer is A. (10) / स्थिर पदों का योग. ( (x+4)(x+6)=x-2 +10x+24 ). Exam tip: the coefficient of (x) comes from the sum of constants.
Step 3
Exam Tip
( (x+4)(x+6)=x-2 +10x+24 ) होता है। परीक्षा में (x) का गुणांक स्थिर पदों के योग से मिलता है।
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( (m+2)2 ) में बीच का पद कौन सा है?
What is the middle term in ( (m+2)2 )?
#middle term
#binomial square
#easy algebra
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A (2m)
B \(m^2\)
C (4)
D (4m)
Explanation opens after your attempt
Step 1
Concept
The middle term is (2ab) so \(2\times m\times2=4m\). Exam tip: distinguish squares from the middle term.
Step 2
Why this answer is correct
The correct answer is D. (4m). The middle term is (2ab) so \(2\times m\times2=4m\). Exam tip: distinguish squares from the middle term.
Step 3
Exam Tip
बीच का पद (2ab) होता है इसलिए \(2\times m\times2=4m\)। परीक्षा में वर्ग और बीच का पद अलग पहचानें।
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\(49^2\) को ( (50-1)2 ) से निकालने पर मान क्या होगा?
Using ( (50-1)2 ), what is the value of \(49^2\)?
#mental math
#49 square
#square identity
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A (2501)
B (2500)
C (2400)
D (2401)
Explanation opens after your attempt
Step 1
Concept
\(49^2=2500-100+1=2401\). Exam tip: subtract (2ab) in the square of a difference.
Step 2
Why this answer is correct
The correct answer is D. (2401). \(49^2=2500-100+1=2401\). Exam tip: subtract (2ab) in the square of a difference.
Step 3
Exam Tip
\(49^2=2500-100+1=2401\) होता है। परीक्षा में घटाव वाले वर्ग में (2ab) घटाएँ।
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( (3a+b)2 ) का विस्तार क्या होगा?
What will be the expansion of ( (3a+b)2 )?
#binomial square
#algebraic expansion
#identity
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A \(9a^2+6ab+b^2\)
B \(3a^2+6ab+b^2\)
C \(9a^2+b^2\)
D \(9a^2-6ab+b^2\)
Explanation opens after your attempt
Correct Answer
A. \(9a^2+6ab+b^2\)
Step 1
Concept
The square of the first term is \(9a^2\) and the middle term is (6ab). Exam tip: write the square of (3a) as \(9a^2\).
Step 2
Why this answer is correct
The correct answer is A. \(9a^2+6ab+b^2\). The square of the first term is \(9a^2\) and the middle term is (6ab). Exam tip: write the square of (3a) as \(9a^2\).
Step 3
Exam Tip
पहले पद का वर्ग \(9a^2\) और बीच का पद (6ab) है। परीक्षा में (3a) का वर्ग \(9a^2\) लिखें।
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( (2m+3)2 ) में मध्य पद कौन-सा है?
What is the middle term in ( (2m+3)2 )?
#middle term
#binomial square
#2m plus 3
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A (6m) / आधा पद
B (12m) / सही मध्य पद
C \(4m^2\) / पहला वर्ग
D (9) / अंतिम वर्ग
Explanation opens after your attempt
Correct Answer
B. (12m) / सही मध्य पद
Step 1
Concept
The middle term is \(2\cdot2m\cdot3=12m\). Exam tip: multiply both terms and then multiply by (2).
Step 2
Why this answer is correct
The correct answer is B. (12m) / सही मध्य पद. The middle term is \(2\cdot2m\cdot3=12m\). Exam tip: multiply both terms and then multiply by (2).
Step 3
Exam Tip
मध्य पद \(2\cdot2m\cdot3=12m\) है। परीक्षा में दोनों पदों को गुणा करके (2) से गुणा करें।
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( (2x-3)2 ) का सही रूप चुनिए।
Choose the correct form of ( (2x-3)2 ).
#minus square
#binomial identity
#expansion
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A \(4x^2+12x+9\)
B \(4x^2-12x+9\)
C \(2x^2-6x+9\)
D \(4x^2-9\)
Explanation opens after your attempt
Correct Answer
B. \(4x^2-12x+9\)
Step 1
Concept
In ( (a-b)2 ) the middle term is ( -2ab ). Exam tip: remember \(2\times2x\times3=12x\).
Step 2
Why this answer is correct
The correct answer is B. \(4x^2-12x+9\). In ( (a-b)2 ) the middle term is ( -2ab ). Exam tip: remember \(2\times2x\times3=12x\).
Step 3
Exam Tip
( (a-b)2 ) में बीच का पद ( -2ab ) होता है। परीक्षा में \(2\times2x\times3=12x\) याद रखें।
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\( 51^2 \) को ( (50+1)2 ) से निकालने पर मान क्या है?
What is the value of \( 51^2 \) using ( (50+1)2 )?
#numeric identity
#square calculation
#mental math
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A (2501)
B (2600)
C (2601)
D (2500)
Explanation opens after your attempt
Step 1
Concept
( (50+1)2 =2500+100+1=2601 ). Exam tip: identities make numerical squares faster.
Step 2
Why this answer is correct
The correct answer is C. (2601). ( (50+1)2 =2500+100+1=2601 ). Exam tip: identities make numerical squares faster.
Step 3
Exam Tip
( (50+1)2 =2500+100+1=2601 )। परीक्षा में संख्यात्मक वर्ग में पहचान से गणना तेज होती है।
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\( 49^2 \) को ( (50-1)2 ) से निकालिए।
Find \( 49^2 \) using ( (50-1)2 ).
#numeric square
#minus identity
#calculation
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A (2401)
B (2499)
C (2501)
D (2301)
Explanation opens after your attempt
Step 1
Concept
( (50-1)2 =2500-100+1=2401 ). Exam tip: the middle term is subtracted in ( (a-b)2 ).
Step 2
Why this answer is correct
The correct answer is A. (2401). ( (50-1)2 =2500-100+1=2401 ). Exam tip: the middle term is subtracted in ( (a-b)2 ).
Step 3
Exam Tip
( (50-1)2 =2500-100+1=2401 )। परीक्षा में ( (a-b)2 ) में बीच का पद घटता है।
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\( 103^2 \) का मान पहचान से क्या होगा?
What is the value of \( 103^2 \) using an identity?
#square calculation
#numeric identity
#algebra
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A (10609)
B (10600)
C (10900)
D (10690)
Explanation opens after your attempt
Correct Answer
A. (10609)
Step 1
Concept
(103=100+3) so ( (100+3)2 =10609 ). Exam tip: split the number near an easy square.
Step 2
Why this answer is correct
The correct answer is A. (10609). (103=100+3) so ( (100+3)2 =10609 ). Exam tip: split the number near an easy square.
Step 3
Exam Tip
(103=100+3) इसलिए ( (100+3)2 =10609 )। परीक्षा में संख्या को पास के आसान वर्ग में तोड़ें।
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\( 98^2 \) को ( (100-2)2 ) से निकालने पर उत्तर क्या है?
What is the answer for \( 98^2 \) using ( (100-2)2 )?
#numeric square
#algebraic identity
#mental calculation
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A (9804)
B (9604)
C (9404)
D (10004)
Explanation opens after your attempt
Step 1
Concept
( (100-2)2 =10000-400+4=9604 ). Exam tip: keep the subtracted middle term correct.
Step 2
Why this answer is correct
The correct answer is B. (9604). ( (100-2)2 =10000-400+4=9604 ). Exam tip: keep the subtracted middle term correct.
Step 3
Exam Tip
( (100-2)2 =10000-400+4=9604 )। परीक्षा में घटाने वाले बीच के पद को सही रखें।
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( (x+8)2 -x-2 ) को सरल कीजिए।
Simplify ( (x+8)2 -x-2 ).
#simplification
#square identity
#like terms
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A (8x+64)
B (16x+8)
C (16x+64)
D \(x^2+64\)
Explanation opens after your attempt
Correct Answer
C. (16x+64)
Step 1
Concept
( (x+8)2 =x-2 +16x+64 ) and then \(x^2\) cancels. Exam tip: do not forget to cancel like terms.
Step 2
Why this answer is correct
The correct answer is C. (16x+64). ( (x+8)2 =x-2 +16x+64 ) and then \(x^2\) cancels. Exam tip: do not forget to cancel like terms.
Step 3
Exam Tip
( (x+8)2 =x-2 +16x+64 ) से \(x^2\) घटता है। परीक्षा में समान पदों को काटना न भूलें।
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( (a+6)2 -(a-6)2 ) का सरल रूप क्या है?
What is the simplified form of ( (a+6)2 -(a-6)2 )?
#difference of squares
#simplification
#algebra
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A (12a)
B (24a)
C (36a)
D \(a^2+36\)
Explanation opens after your attempt
Step 1
Concept
On expansion \(a^2+12a+36-a^2+12a-36=24a\). Exam tip: apply the minus sign to the whole bracket.
Step 2
Why this answer is correct
The correct answer is B. (24a). On expansion \(a^2+12a+36-a^2+12a-36=24a\). Exam tip: apply the minus sign to the whole bracket.
Step 3
Exam Tip
विस्तार करने पर \(a^2+12a+36-a^2+12a-36=24a\) मिलता है। परीक्षा में ऋण चिन्ह पूरे कोष्ठक पर लागू करें।
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( (r+9)(r-9) ) का गुणनफल क्या है?
What is the product of ( (r+9)(r-9) )?
#product identity
#difference of squares
#binomial
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A \(r^2+81\)
B \(r^2-18r+81\)
C \(r^2-81\)
D \(r^2+18r+81\)
Explanation opens after your attempt
Correct Answer
C. \(r^2-81\)
Step 1
Concept
This is the \(a^2-b^2\) form. Exam tip: remember \(9^2=81\).
Step 2
Why this answer is correct
The correct answer is C. \(r^2-81\). This is the \(a^2-b^2\) form. Exam tip: remember \(9^2=81\).
Step 3
Exam Tip
यह \(a^2-b^2\) वाला रूप है। परीक्षा में \(9^2=81\) ध्यान रखें।
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\( 72\times68 \) को पहचान से निकालिए।
Find \( 72\times68 \) using an identity.
#difference of squares
#numeric product
#identity
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A (4896)
B (4900)
C (4800)
D (4796)
Explanation opens after your attempt
Step 1
Concept
(72\times68=(70+2)(70-2)=702 -22 =4896). Exam tip: choose the nearby common number.
Step 2
Why this answer is correct
The correct answer is A. (4896). (72\times68=(70+2)(70-2)=702 -22 =4896). Exam tip: choose the nearby common number.
Step 3
Exam Tip
(72\times68=(70+2)(70-2)=702 -22 =4896)। परीक्षा में पास की समान संख्या चुनें।
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\( 64^2-36^2 \) का मान क्या है?
What is the value of \( 64^2-36^2 \)?
#difference of squares
#numeric value
#identity
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A (1800)
B (2800)
C (3000)
D (2000)
Explanation opens after your attempt
Step 1
Concept
Using (a-2 -b-2 =(a+b)(a-b)), we get \(100\times28=2800\). Exam tip: convert difference of squares into a product.
Step 2
Why this answer is correct
The correct answer is B. (2800). Using (a-2 -b-2 =(a+b)(a-b)), we get \(100\times28=2800\). Exam tip: convert difference of squares into a product.
Step 3
Exam Tip
(a-2 -b-2 =(a+b)(a-b)) से \(100\times28=2800\)। परीक्षा में अंतर वर्ग को गुणनफल में बदलें।
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\( x^2+12x+36 \) किसका वर्ग है?
\( x^2+12x+36 \) is the square of what?
#perfect square
#factorization
#algebra
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A ( (x+12)2 )
B ( (x-6)2 )
C ( (x+6)2 )
D ( (x-12)2 )
Explanation opens after your attempt
Correct Answer
C. ( (x+6)2 )
Step 1
Concept
It is \(x^2+2\times x\times6+6^2\). Exam tip: use the square root of the last term to identify the bracket.
Step 2
Why this answer is correct
The correct answer is C. ( (x+6)2 ). It is \(x^2+2\times x\times6+6^2\). Exam tip: use the square root of the last term to identify the bracket.
Step 3
Exam Tip
यह \(x^2+2\times x\times6+6^2\) है। परीक्षा में अंतिम पद के वर्गमूल से कोष्ठक पहचानें।
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\( t^2-14t+49 \) किसके बराबर है?
What is \( t^2-14t+49 \) equal to?
#perfect square
#minus square
#factorization
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A ( (t+7)2 )
B ( (t-7)2 )
C ( (t-14)2 )
D ( (t+49)2 )
Explanation opens after your attempt
Correct Answer
B. ( (t-7)2 )
Step 1
Concept
It is \(t^2-2\times t\times7+7^2\). Exam tip: choose ( (a-b)2 ) when the middle term is negative.
Step 2
Why this answer is correct
The correct answer is B. ( (t-7)2 ). It is \(t^2-2\times t\times7+7^2\). Exam tip: choose ( (a-b)2 ) when the middle term is negative.
Step 3
Exam Tip
यह \(t^2-2\times t\times7+7^2\) है। परीक्षा में बीच का ऋण चिन्ह देखकर ( (a-b)2 ) चुनें।
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\( x^2-64 \) का गुणनखंड रूप क्या है?
What is the factor form of \( x^2-64 \)?
#factorization
#difference of squares
#algebraic identities
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A ( (x+8)2 )
B ( (x-8)2 )
C ( (x+64)(x-1) )
D ( (x+8)(x-8) )
Explanation opens after your attempt
Correct Answer
D. ( (x+8)(x-8) )
Step 1
Concept
Since \(64=8^2\), (x-2 -64=(x+8)(x-8)). Exam tip: identify difference of squares quickly.
Step 2
Why this answer is correct
The correct answer is D. ( (x+8)(x-8) ). Since \(64=8^2\), (x-2 -64=(x+8)(x-8)). Exam tip: identify difference of squares quickly.
Step 3
Exam Tip
\(64=8^2\) इसलिए (x-2 -64=(x+8)(x-8))। परीक्षा में अंतर वर्ग तुरंत पहचानें।
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\( 4x^2-25 \) का गुणनखंड क्या है?
What are the factors of \( 4x^2-25 \)?
#difference of squares
#factorization
#identity
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A ( (2x+5)(2x-5) )
B ( (4x+5)(x-5) )
C ( (2x-5)2 )
D ( (x+5)(x-5) )
Explanation opens after your attempt
Correct Answer
A. ( (2x+5)(2x-5) )
Step 1
Concept
(4x-2 =(2x)2 ) and \(25=5^2\). Exam tip: write both terms as squares.
Step 2
Why this answer is correct
The correct answer is A. ( (2x+5)(2x-5) ). (4x-2 =(2x)2 ) and \(25=5^2\). Exam tip: write both terms as squares.
Step 3
Exam Tip
(4x-2 =(2x)2 ) और \(25=5^2\) है। परीक्षा में दोनों पदों को वर्ग के रूप में लिखें।
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( (x+3)(x-4) ) का सही विस्तार कौन सा है?
Which is the correct expansion of ( (x+3)(x-4) )?
#product identity
#signed terms
#expansion
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A \(x^2+x-12\)
B \(x^2-x-12\)
C \(x^2+7x-12\)
D \(x^2-12\)
Explanation opens after your attempt
Correct Answer
B. \(x^2-x-12\)
Step 1
Concept
(3+(-4)=-1) and \(3\times(-4)=-12\). Exam tip: be careful while adding negative numbers.
Step 2
Why this answer is correct
The correct answer is B. \(x^2-x-12\). (3+(-4)=-1) and \(3\times(-4)=-12\). Exam tip: be careful while adding negative numbers.
Step 3
Exam Tip
(3+(-4)=-1) और \(3\times(-4)=-12\)। परीक्षा में ऋण संख्या जोड़ते समय सावधान रहें।
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( (x-6)(x-2) ) का विस्तार क्या होगा?
What will be the expansion of ( (x-6)(x-2) )?
#binomial product
#negative terms
#expansion
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A \(x^2-8x+12\)
B \(x^2+8x+12\)
C \(x^2-4x-12\)
D \(x^2-12x+8\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-8x+12\)
Step 1
Concept
((-6)+(-2)=-8) and ((-6)(-2)=12). Exam tip: product of two negative terms is positive.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-8x+12\). ((-6)+(-2)=-8) and ((-6)(-2)=12). Exam tip: product of two negative terms is positive.
Step 3
Exam Tip
((-6)+(-2)=-8) और ((-6)(-2)=12)। परीक्षा में दो ऋण पदों का गुणन धनात्मक होता है।
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( (z+1)(z+9) ) में (z) का गुणांक क्या है?
What is the coefficient of (z) in ( (z+1)(z+9) )?
#coefficient
#product identity
#algebra
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A (9)
B (1)
C (10)
D (90)
Explanation opens after your attempt
Step 1
Concept
( (z+1)(z+9)=z-2 +10z+9 ). Exam tip: the coefficient of (z) comes from the sum of the constants.
Step 2
Why this answer is correct
The correct answer is C. (10). ( (z+1)(z+9)=z-2 +10z+9 ). Exam tip: the coefficient of (z) comes from the sum of the constants.
Step 3
Exam Tip
( (z+1)(z+9)=z-2 +10z+9 ) होता है। परीक्षा में (z) का गुणांक दोनों स्थिर पदों के योग से मिलता है।
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( (x+y+z)2 ) में (2xy) के साथ कौन से और मिश्र पद आते हैं?
In ( (x+y+z)2 ), which other mixed terms come with (2xy)?
#three term identity
#mixed terms
#algebra
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A (2xz) और (2yz) / (2xz) and (2yz)
B \(x^2\) और \(y^2\) / \(x^2\) and \(y^2\)
C \(z^2\) और (xy) / \(z^2\) and (xy)
D (xyz) और (x+y) / (xyz) and (x+y)
Explanation opens after your attempt
Correct Answer
A. (2xz) और (2yz) / (2xz) and (2yz)
Step 1
Concept
In the square of three terms, mixed terms are (2xy), (2yz), and (2zx). Exam tip: include all pairs.
Step 2
Why this answer is correct
The correct answer is A. (2xz) और (2yz) / (2xz) and (2yz). In the square of three terms, mixed terms are (2xy), (2yz), and (2zx). Exam tip: include all pairs.
Step 3
Exam Tip
तीन पदों के वर्ग में मिश्र पद (2xy), (2yz), और (2zx) होते हैं। परीक्षा में सभी जोड़ों को शामिल करें।
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( (a+b+c)2 ) का सही विस्तार कौन सा है?
Which is the correct expansion of ( (a+b+c)2 )?
#three term square
#algebraic identity
#expansion
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A \(a^2+b^2+c^2+2ab+2bc+2ca\)
B \(a^2+b^2+c^2+abc\)
C \(a^2+b^2+c^2+ab+bc+ca\)
D \(a^2-b^2+c^2\)
Explanation opens after your attempt
Correct Answer
A. \(a^2+b^2+c^2+2ab+2bc+2ca\)
Step 1
Concept
Each pair gives a double mixed term in three terms. Exam tip: do not miss (2ab), (2bc), and (2ca).
Step 2
Why this answer is correct
The correct answer is A. \(a^2+b^2+c^2+2ab+2bc+2ca\). Each pair gives a double mixed term in three terms. Exam tip: do not miss (2ab), (2bc), and (2ca).
Step 3
Exam Tip
तीन पदों में प्रत्येक जोड़े का दुगुना मिश्र पद आता है। परीक्षा में (2ab), (2bc), और (2ca) न छोड़ें।
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( (x+1)2 ) और \(x^2+1\) में क्या अंतर है?
What is the difference between ( (x+1)2 ) and \(x^2+1\)?
#middle term
#common mistake
#binomial square
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A (x)
B (2x)
C (1)
D \(x^2\)
Explanation opens after your attempt
Step 1
Concept
( (x+1)2 =x-2 +2x+1 ), so the difference is (2x). Exam tip: do not forget the middle term while expanding.
Step 2
Why this answer is correct
The correct answer is B. (2x). ( (x+1)2 =x-2 +2x+1 ), so the difference is (2x). Exam tip: do not forget the middle term while expanding.
Step 3
Exam Tip
( (x+1)2 =x-2 +2x+1 ) है इसलिए अंतर (2x) है। परीक्षा में वर्ग खोलते समय बीच का पद न भूलें।
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( (5x+2)2 ) में स्थिर पद क्या है?
What is the constant term in ( (5x+2)2 )?
#constant term
#square expansion
#algebra
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A \(25x^2\)
B (20x)
C (4)
D (10x)
Explanation opens after your attempt
Step 1
Concept
The constant term is \(2^2=4\). Exam tip: a constant term has no (x).
Step 2
Why this answer is correct
The correct answer is C. (4). The constant term is \(2^2=4\). Exam tip: a constant term has no (x).
Step 3
Exam Tip
स्थिर पद \(2^2=4\) होता है। परीक्षा में स्थिर पद वह होता है जिसमें (x) न हो।
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( (4p-1)2 ) में (p) वाला पद कौन सा है?
Which term contains (p) in ( (4p-1)2 )?
#middle term
#negative sign
#binomial square
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A (8p)
B (-8p)
C \(16p^2\)
D (1)
Explanation opens after your attempt
Step 1
Concept
The middle term is \(-2\times4p\times1=-8p\). Exam tip: the sign is very important in a subtraction square.
Step 2
Why this answer is correct
The correct answer is B. (-8p). The middle term is \(-2\times4p\times1=-8p\). Exam tip: the sign is very important in a subtraction square.
Step 3
Exam Tip
बीच का पद \(-2\times4p\times1=-8p\) है। परीक्षा में घटाव वाले वर्ग में चिन्ह बहुत महत्वपूर्ण है।
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\( 1002^2 \) निकालने के लिए कौन सा रूप सबसे उपयोगी है?
Which form is most useful to find \( 1002^2 \)?
#numeric identity
#square method
#easy calculation
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A ( (1000+2)2 )
B ( (1000-2)2 )
C ( (100+2)2 )
D ( (10+2)2 )
Explanation opens after your attempt
Correct Answer
A. ( (1000+2)2 )
Step 1
Concept
Writing (1002) as (1000+2) is easy. Exam tip: connect a large number to a nearby simple number.
Step 2
Why this answer is correct
The correct answer is A. ( (1000+2)2 ). Writing (1002) as (1000+2) is easy. Exam tip: connect a large number to a nearby simple number.
Step 3
Exam Tip
(1002) को (1000+2) लिखना आसान है। परीक्षा में बड़ी संख्या को निकट सरल संख्या से जोड़ें।
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\( 999^2 \) निकालने के लिए कौन सा रूप सही है?
Which form is correct to find \( 999^2 \)?
#numeric square
#minus square
#identity
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A ( (900+99)2 )
B ( (1000-1)2 )
C ( (1000+1)2 )
D ( (99+9)2 )
Explanation opens after your attempt
Correct Answer
B. ( (1000-1)2 )
Step 1
Concept
Write (999) as (1000-1) and use ( (a-b)2 ). Exam tip: choosing the nearest simple number is faster.
Step 2
Why this answer is correct
The correct answer is B. ( (1000-1)2 ). Write (999) as (1000-1) and use ( (a-b)2 ). Exam tip: choosing the nearest simple number is faster.
Step 3
Exam Tip
(999) को (1000-1) लिखकर ( (a-b)2 ) लगाएँ। परीक्षा में निकटतम सरल संख्या चुनना तेज तरीका है।
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( (u+v)(u-v) ) में कौन सा पद नहीं आता?
Which term does not appear in ( (u+v)(u-v) )?
#difference of squares
#cancel terms
#identity
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A \(u^2\)
B \(-v^2\)
C (uv)
D \(u^2-v^2\)
Explanation opens after your attempt
Step 1
Concept
The middle (uv) terms cancel. Exam tip: mixed terms do not remain in opposite-sign products.
Step 2
Why this answer is correct
The correct answer is C. (uv). The middle (uv) terms cancel. Exam tip: mixed terms do not remain in opposite-sign products.
Step 3
Exam Tip
मध्य के (uv) पद कट जाते हैं। परीक्षा में विपरीत चिन्ह वाले गुणन में मिश्र पद नहीं बचता।
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( (q+10)2 ) में \(q^2\) और (100) के अलावा कौन सा पद आएगा?
In ( (q+10)2 ), which term comes besides \(q^2\) and (100)?
#middle term
#square identity
#algebra
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A (10q)
B (20q)
C (100q)
D (q)
Explanation opens after your attempt
Step 1
Concept
The middle term is \(2\times q\times10=20q\). Exam tip: remember to multiply by two.
Step 2
Why this answer is correct
The correct answer is B. (20q). The middle term is \(2\times q\times10=20q\). Exam tip: remember to multiply by two.
Step 3
Exam Tip
बीच का पद \(2\times q\times10=20q\) है। परीक्षा में दो गुना गुणन करना याद रखें।
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( (n-11)2 ) में अंतिम पद क्या होगा?
What will be the last term in ( (n-11)2 )?
#last term
#minus square
#algebraic identity
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A (11n)
B (-121)
C (121)
D (-22n)
Explanation opens after your attempt
Step 1
Concept
The last term \(11^2=121\) is always positive. Exam tip: the square term remains positive.
Step 2
Why this answer is correct
The correct answer is C. (121). The last term \(11^2=121\) is always positive. Exam tip: the square term remains positive.
Step 3
Exam Tip
अंतिम पद \(11^2=121\) हमेशा धनात्मक होता है। परीक्षा में वर्ग का चिन्ह धनात्मक रहता है।
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( (2a+3b)2 ) में मिश्र पद क्या है?
What is the mixed term in ( (2a+3b)2 )?
#mixed term
#binomial square
#coefficients
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A (5ab)
B (6ab)
C (12ab)
D \(9b^2\)
Explanation opens after your attempt
Step 1
Concept
The mixed term is \(2\times2a\times3b=12ab\). Exam tip: multiply the coefficients too.
Step 2
Why this answer is correct
The correct answer is C. (12ab). The mixed term is \(2\times2a\times3b=12ab\). Exam tip: multiply the coefficients too.
Step 3
Exam Tip
मिश्र पद \(2\times2a\times3b=12ab\) है। परीक्षा में गुणांक भी साथ गुणा करें।
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( (3x-2y)2 ) का विस्तार क्या है?
What is the expansion of ( (3x-2y)2 )?
#binomial square
#two variables
#expansion
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A \(9x^2-12xy+4y^2\)
B \(9x^2+12xy+4y^2\)
C \(3x^2-12xy+2y^2\)
D \(9x^2-4y^2\)
Explanation opens after your attempt
Correct Answer
A. \(9x^2-12xy+4y^2\)
Step 1
Concept
In ( (a-b)2 ) the mixed term is negative. Exam tip: write ((3x)2 =9x-2 ) and ((2y)2 =4y-2 ).
Step 2
Why this answer is correct
The correct answer is A. \(9x^2-12xy+4y^2\). In ( (a-b)2 ) the mixed term is negative. Exam tip: write ((3x)2 =9x-2 ) and ((2y)2 =4y-2 ).
Step 3
Exam Tip
( (a-b)2 ) में मिश्र पद ऋणात्मक होता है। परीक्षा में ((3x)2 =9x-2 ) और ((2y)2 =4y-2 ) लिखें।
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( (5m+4n)(5m-4n) ) का मान क्या है?
What is the value of ( (5m+4n)(5m-4n) )?
#difference of squares
#two variables
#product
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A \(25m^2+16n^2\)
B \(25m^2-16n^2\)
C (10m-8n)
D \(25m^2-40mn+16n^2\)
Explanation opens after your attempt
Correct Answer
B. \(25m^2-16n^2\)
Step 1
Concept
This is a direct use of \(a^2-b^2\). Exam tip: use ((5m)2 =25m-2 ) and ((4n)2 =16n-2 ).
Step 2
Why this answer is correct
The correct answer is B. \(25m^2-16n^2\). This is a direct use of \(a^2-b^2\). Exam tip: use ((5m)2 =25m-2 ) and ((4n)2 =16n-2 ).
Step 3
Exam Tip
यह \(a^2-b^2\) का सीधा प्रयोग है। परीक्षा में ((5m)2 =25m-2 ) और ((4n)2 =16n-2 ) करें।
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\( x^2+18x+81 \) का वर्ग रूप कौन सा है?
Which square form represents \( x^2+18x+81 \)?
#perfect square
#recognition
#algebraic identity
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A ( (x+9)2 )
B ( (x-9)2 )
C ( (x+18)2 )
D ( (x+81)2 )
Explanation opens after your attempt
Correct Answer
A. ( (x+9)2 )
Step 1
Concept
\(81=9^2\) and the middle term \(18x=2\times x\times9\). Exam tip: identify the number from the last term.
Step 2
Why this answer is correct
The correct answer is A. ( (x+9)2 ). \(81=9^2\) and the middle term \(18x=2\times x\times9\). Exam tip: identify the number from the last term.
Step 3
Exam Tip
\(81=9^2\) और बीच का पद \(18x=2\times x\times9\) है। परीक्षा में अंतिम पद से संख्या पहचानें।
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\( k^2-20k+100 \) किसका वर्ग है?
\( k^2-20k+100 \) is the square of what?
#perfect square
#minus identity
#factorization
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A ( (k+20)2 )
B ( (k-10)2 )
C ( (k+10)2 )
D ( (k-100)2 )
Explanation opens after your attempt
Correct Answer
B. ( (k-10)2 )
Step 1
Concept
\(100=10^2\) and the middle term is \(-20k=-2\times k\times10\). Exam tip: identify the negative middle term.
Step 2
Why this answer is correct
The correct answer is B. ( (k-10)2 ). \(100=10^2\) and the middle term is \(-20k=-2\times k\times10\). Exam tip: identify the negative middle term.
Step 3
Exam Tip
\(100=10^2\) और बीच का पद \(-20k=-2\times k\times10\) है। परीक्षा में ऋणात्मक बीच का पद पहचानें।
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\( 37^2-27^2 \) का मान क्या है?
What is the value of \( 37^2-27^2 \)?
#numeric difference
#square identity
#calculation
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A (540)
B (600)
C (640)
D (720)
Explanation opens after your attempt
Step 1
Concept
(372 -272 =(37+27)(37-27)=64\times10=640). Exam tip: difference of squares makes multiplication easy.
Step 2
Why this answer is correct
The correct answer is C. (640). (372 -272 =(37+27)(37-27)=64\times10=640). Exam tip: difference of squares makes multiplication easy.
Step 3
Exam Tip
(372 -272 =(37+27)(37-27)=64\times10=640)। परीक्षा में अंतर वर्ग से गुणा आसान होता है।
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\( 45\times55 \) को किस पहचान से जल्दी निकाला जा सकता है?
Which identity can quickly find \( 45\times55 \)?
#numeric product
#difference of squares
#identity choice
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A ( (a+b)2 )
B ( (a-b)2 )
C ( (a+b)(a-b)=a-2 -b-2 )
D ( (a+b+c)2 )
Explanation opens after your attempt
Correct Answer
C. ( (a+b)(a-b)=a-2 -b-2 )
Step 1
Concept
(45\times55=(50-5)(50+5)). Exam tip: use difference of squares for numbers around the same centre.
Step 2
Why this answer is correct
The correct answer is C. ( (a+b)(a-b)=a-2 -b-2 ). (45\times55=(50-5)(50+5)). Exam tip: use difference of squares for numbers around the same centre.
Step 3
Exam Tip
(45\times55=(50-5)(50+5)) है। परीक्षा में समान केंद्र वाली संख्याएँ अंतर वर्ग से करें।
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( (a+2b+c)2 ) में \(4b^2\) किससे आता है?
In ( (a+2b+c)2 ), where does \(4b^2\) come from?
#three term square
#coefficient square
#identity
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A \(a^2\) से / From \(a^2\)
B ((2b)2 ) से / From ((2b)2 )
C \(c^2\) से / From \(c^2\)
D (2ac) से / From (2ac)
Explanation opens after your attempt
Correct Answer
B. ((2b)2 ) से / From ((2b)2 )
Step 1
Concept
The square of (2b) is ((2b)2 =4b-2 ). Exam tip: square the coefficient too.
Step 2
Why this answer is correct
The correct answer is B. ((2b)2 ) से / From ((2b)2 ). The square of (2b) is ((2b)2 =4b-2 ). Exam tip: square the coefficient too.
Step 3
Exam Tip
(2b) का वर्ग ((2b)2 =4b-2 ) होता है। परीक्षा में गुणांक का भी वर्ग करें।
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( (x+y+2)2 ) में स्थिर पद क्या होगा?
What will be the constant term in ( (x+y+2)2 )?
#constant term
#three term square
#algebra
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A (2)
B (4)
C (2x)
D (4xy)
Explanation opens after your attempt
Step 1
Concept
The constant term is \(2^2=4\). Exam tip: the term containing only a number is called the constant term.
Step 2
Why this answer is correct
The correct answer is B. (4). The constant term is \(2^2=4\). Exam tip: the term containing only a number is called the constant term.
Step 3
Exam Tip
स्थिर पद \(2^2=4\) है। परीक्षा में केवल संख्या वाले पद को स्थिर पद कहते हैं।
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( (x-3)(x+3)+9 ) को सरल कीजिए।
Simplify ( (x-3)(x+3)+9 ).
#simplification
#difference of squares
#algebra
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A \(x^2\)
B \(x^2-9\)
C \(x^2+9\)
D \(x^2+18\)
Explanation opens after your attempt
Correct Answer
A. \(x^2\)
Step 1
Concept
( (x-3)(x+3)=x-2 -9 ) and then (+9) gives \(x^2\). Exam tip: identify the product first.
Step 2
Why this answer is correct
The correct answer is A. \(x^2\). ( (x-3)(x+3)=x-2 -9 ) and then (+9) gives \(x^2\). Exam tip: identify the product first.
Step 3
Exam Tip
( (x-3)(x+3)=x-2 -9 ) और फिर (+9) से \(x^2\) मिलता है। परीक्षा में पहले गुणनफल पहचानें।
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( (2x+1)2 -(2x-1)2 ) का मान क्या है?
What is the value of ( (2x+1)2 -(2x-1)2 )?
#difference of squares
#identity shortcut
#simplification
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A (2x)
B (4x)
C (8x)
D (16x)
Explanation opens after your attempt
Step 1
Concept
This is (4ab) where (a=2x) and (b=1). Exam tip: calculate \(4\times2x\times1=8x\).
Step 2
Why this answer is correct
The correct answer is C. (8x). This is (4ab) where (a=2x) and (b=1). Exam tip: calculate \(4\times2x\times1=8x\).
Step 3
Exam Tip
यह (4ab) है जहाँ (a=2x) और (b=1)। परीक्षा में \(4\times2x\times1=8x\) करें।
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( (x+7)(x+7) ) को पहचान के रूप में कैसे लिखेंगे?
How will you write ( (x+7)(x+7) ) as an identity form?
#square form
#binomial
#identity recognition
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A ( (x+7)2 )
B ( (x-7)2 )
C \(x^2-49\)
D ( (x+7)(x-7) )
Explanation opens after your attempt
Correct Answer
A. ( (x+7)2 )
Step 1
Concept
The product of two identical factors is a square. Exam tip: treat ( (x+7)(x+7) ) as ( (x+7)2 ).
Step 2
Why this answer is correct
The correct answer is A. ( (x+7)2 ). The product of two identical factors is a square. Exam tip: treat ( (x+7)(x+7) ) as ( (x+7)2 ).
Step 3
Exam Tip
समान दो गुणनखंडों का गुणन वर्ग होता है। परीक्षा में ( (x+7)(x+7) ) को ( (x+7)2 ) मानें।
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( (a-b)2 ) और \(a^2-b^2\) में मुख्य अंतर क्या है?
What is the main difference between ( (a-b)2 ) and \(a^2-b^2\)?
#common mistake
#minus square
#difference of squares
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A दोनों हमेशा समान हैं / Both are always same
B ( (a-b)2 ) में (-2ab) पद होता है पर \(a^2-b^2\) में नहीं / ( (a-b)2 ) has (-2ab) term but \(a^2-b^2\) does not
C \(a^2-b^2\) में (+2ab) होता है / \(a^2-b^2\) has (+2ab)
D दोनों में कोई वर्ग पद नहीं होता / Neither has square terms
Explanation opens after your attempt
Correct Answer
B. ( (a-b)2 ) में (-2ab) पद होता है पर \(a^2-b^2\) में नहीं / ( (a-b)2 ) has (-2ab) term but \(a^2-b^2\) does not
Step 1
Concept
( (a-b)2 =a-2 -2ab+b-2 ) while (a-2 -b-2 =(a+b)(a-b)). Exam tip: keep square of bracket and difference of squares separate.
Step 2
Why this answer is correct
The correct answer is B. ( (a-b)2 ) में (-2ab) पद होता है पर \(a^2-b^2\) में नहीं / ( (a-b)2 ) has (-2ab) term but \(a^2-b^2\) does not. ( (a-b)2 =a-2 -2ab+b-2 ) while (a-2 -b-2 =(a+b)(a-b)). Exam tip: keep square of bracket and difference of squares separate.
Step 3
Exam Tip
( (a-b)2 =a-2 -2ab+b-2 ) जबकि (a-2 -b-2 =(a+b)(a-b)) है। परीक्षा में कोष्ठक के वर्ग और अंतर वर्ग को अलग रखें।
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