( (2x+3)2 ) का सही प्रसार कौन सा है?
What is the correct expansion of ( (2x+3)2 )?
#algebraic identities
#binomial square
#expansion
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A \(4x^2+12x+9\)
B \(4x^2+6x+9\)
C \(2x^2+12x+9\)
D \(4x^2-12x+9\)
Explanation opens after your attempt
Correct Answer
A. \(4x^2+12x+9\)
Step 1
Concept
Here (a=2x) and (b=3). Since (2ab=12x), the correct expansion is \(4x^2+12x+9\).
Step 2
Why this answer is correct
The correct answer is A. \(4x^2+12x+9\). Here (a=2x) and (b=3). Since (2ab=12x), the correct expansion is \(4x^2+12x+9\).
Step 3
Exam Tip
यहाँ (a=2x) और (b=3) है। (2ab=12x) इसलिए सही प्रसार \(4x^2+12x+9\) है।
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( (x+7)(x-2) ) का प्रसार चुनिए।
Choose the expansion of ( (x+7)(x-2) ).
#binomial product
#coefficient
#constant term
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A \(x^2+9x-14\)
B \(x^2-5x-14\)
C \(x^2+5x-14\)
D \(x^2+5x+14\)
Explanation opens after your attempt
Correct Answer
C. \(x^2+5x-14\)
Step 1
Concept
The coefficient of (x) is (7-2=5) and the constant term is (7\cdot(-2)=-14). Exam tip: watch the signs.
Step 2
Why this answer is correct
The correct answer is C. \(x^2+5x-14\). The coefficient of (x) is (7-2=5) and the constant term is (7\cdot(-2)=-14). Exam tip: watch the signs.
Step 3
Exam Tip
(x) का गुणांक (7-2=5) और स्थिर पद (7\cdot(-2)=-14) है। परीक्षा में चिन्हों का ध्यान रखें।
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( (5a+2b)(5a-2b) ) किसके बराबर है?
What is ( (5a+2b)(5a-2b) ) equal to?
#difference of squares
#product identity
#factorisation
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A \(25a^2+4b^2\)
B \(10a^2-4b^2\)
C \(25a^2-20ab+4b^2\)
D \(25a^2-4b^2\)
Explanation opens after your attempt
Correct Answer
D. \(25a^2-4b^2\)
Step 1
Concept
This is the identity form \(a^2-b^2\). ((5a)2 =25a-2 ) and ((2b)2 =4b-2 ).
Step 2
Why this answer is correct
The correct answer is D. \(25a^2-4b^2\). This is the identity form \(a^2-b^2\). ((5a)2 =25a-2 ) and ((2b)2 =4b-2 ).
Step 3
Exam Tip
यह \(a^2-b^2\) वाली सर्वसमिका का रूप है। ((5a)2 =25a-2 ) और ((2b)2 =4b-2 ) है।
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\( 98^2 \) को सर्वसमिका से निकालने के लिए सबसे अच्छा रूप कौन सा है?
Which is the best form to find \( 98^2 \) using an identity?
#mental math
#minus square
#algebraic identity
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A ( (100-2)2 )
B ( (90+8)2 )
C ( (50+48)2 )
D ( (98+2)2 )
Explanation opens after your attempt
Correct Answer
A. ( (100-2)2 )
Step 1
Concept
Writing (98=100-2) makes calculation easy. Exam tip: choose a nearby round number.
Step 2
Why this answer is correct
The correct answer is A. ( (100-2)2 ). Writing (98=100-2) makes calculation easy. Exam tip: choose a nearby round number.
Step 3
Exam Tip
(98=100-2) लिखने से गणना आसान होती है। परीक्षा में नजदीकी गोल संख्या चुनना उपयोगी है।
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\( x^2+16x+64 \) किसका पूर्ण वर्ग है?
\( x^2+16x+64 \) is the perfect square of what?
#perfect square
#trinomial
#recognition
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A ( (x+16)2 )
B ( (x+8)2 )
C ( (x-8)2 )
D ( (x+64)2 )
Explanation opens after your attempt
Correct Answer
B. ( (x+8)2 )
Step 1
Concept
\(64=8^2\) and \(16x=2\cdot x\cdot8\). Therefore it is ( (x+8)2 ).
Step 2
Why this answer is correct
The correct answer is B. ( (x+8)2 ). \(64=8^2\) and \(16x=2\cdot x\cdot8\). Therefore it is ( (x+8)2 ).
Step 3
Exam Tip
\(64=8^2\) और \(16x=2\cdot x\cdot8\) है। इसलिए यह ( (x+8)2 ) है।
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\( p^2-18p+81 \) का गुणनखंड रूप क्या है?
What is the factor form of \( p^2-18p+81 \)?
#factorisation
#perfect square
#minus square
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A ( (p+9)2 )
B ( (p-18)2 )
C ( (p-9)2 )
D ( (p-81)2 )
Explanation opens after your attempt
Correct Answer
C. ( (p-9)2 )
Step 1
Concept
\(81=9^2\) and the middle term is (-18p). So it is ( (p-9)2 ).
Step 2
Why this answer is correct
The correct answer is C. ( (p-9)2 ). \(81=9^2\) and the middle term is (-18p). So it is ( (p-9)2 ).
Step 3
Exam Tip
\(81=9^2\) और बीच का पद (-18p) है। इसलिए यह ( (p-9)2 ) है।
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\( 103\times97 \) का मान निकालने के लिए कौन सी सर्वसमिका उपयोगी है?
Which identity is useful to calculate \( 103\times97 \)?
#difference of squares
#mental calculation
#product
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A ( (a+b)2 )
B ( (a-b)2 )
C ( (x+a)(x+b) )
D ( (a+b)(a-b)=a-2 -b-2 )
Explanation opens after your attempt
Correct Answer
D. ( (a+b)(a-b)=a-2 -b-2 )
Step 1
Concept
(103=100+3) and (97=100-3). So the difference of squares identity is simplest.
Step 2
Why this answer is correct
The correct answer is D. ( (a+b)(a-b)=a-2 -b-2 ). (103=100+3) and (97=100-3). So the difference of squares identity is simplest.
Step 3
Exam Tip
(103=100+3) और (97=100-3) है। इसलिए अंतर के वर्गों की सर्वसमिका सबसे सरल है।
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( (a+b+c)2 ) का सही प्रसार कौन सा है?
What is the correct expansion of ( (a+b+c)2 )?
#three term square
#algebraic identities
#expansion
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A \(a^2+b^2+c^2+2ab+2bc+2ca\)
B \(a^2+b^2+c^2+ab+bc+ca\)
C \(a^2+b^2+c^2-2ab-2bc-2ca\)
D \(a^2+b^2+c^2+3abc\)
Explanation opens after your attempt
Correct Answer
A. \(a^2+b^2+c^2+2ab+2bc+2ca\)
Step 1
Concept
The square of three terms includes all squares and twice each pair product. Exam tip: do not forget (2ab+2bc+2ca).
Step 2
Why this answer is correct
The correct answer is A. \(a^2+b^2+c^2+2ab+2bc+2ca\). The square of three terms includes all squares and twice each pair product. Exam tip: do not forget (2ab+2bc+2ca).
Step 3
Exam Tip
तीन पदों के वर्ग में सभी वर्ग और दो-दो गुणनफल के दोगुने पद आते हैं। परीक्षा में (2ab+2bc+2ca) न भूलें।
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( (2m+n-1)2 ) में (mn) वाला पद क्या है?
What is the (mn)-term in ( (2m+n-1)2 )?
#mn term
#three term square
#algebra
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A (2mn)
B (mn)
C (4mn)
D (-4mn)
Explanation opens after your attempt
Step 1
Concept
From (2m) and (n), \(2\cdot2m\cdot n=4mn\). Exam tip: look only at the related pair.
Step 2
Why this answer is correct
The correct answer is C. (4mn). From (2m) and (n), \(2\cdot2m\cdot n=4mn\). Exam tip: look only at the related pair.
Step 3
Exam Tip
(2m) और (n) से \(2\cdot2m\cdot n=4mn\) मिलता है। परीक्षा में केवल संबंधित जोड़े को देखें।
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( (x-3)(x+8) ) का स्थिर पद क्या है?
What is the constant term of ( (x-3)(x+8) )?
#constant term
#binomial product
#signs
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A (24)
B (5)
C (-5)
D (-24)
Explanation opens after your attempt
Step 1
Concept
The constant term is ((-3)\cdot8=-24). Exam tip: multiply only the numbers for the constant term.
Step 2
Why this answer is correct
The correct answer is D. (-24). The constant term is ((-3)\cdot8=-24). Exam tip: multiply only the numbers for the constant term.
Step 3
Exam Tip
स्थिर पद ((-3)\cdot8=-24) है। परीक्षा में स्थिर पद के लिए केवल संख्याओं को गुणा करें।
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( (x+4)(x+9) ) में (x) का गुणांक क्या है?
What is the coefficient of (x) in ( (x+4)(x+9) )?
#coefficient
#x plus a
#binomial product
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A (13)
B (36)
C (9)
D (4)
Explanation opens after your attempt
Step 1
Concept
In ( (x+a)(x+b) ), the coefficient of (x) is (a+b). Here (4+9=13).
Step 2
Why this answer is correct
The correct answer is A. (13). In ( (x+a)(x+b) ), the coefficient of (x) is (a+b). Here (4+9=13).
Step 3
Exam Tip
( (x+a)(x+b) ) में (x) का गुणांक (a+b) होता है। यहाँ (4+9=13) है।
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( (x-6)(x-5) ) का प्रसार कौन सा है?
Which is the expansion of ( (x-6)(x-5) )?
#binomial product
#negative terms
#expansion
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A \(x^2+11x+30\)
B \(x^2-11x+30\)
C \(x^2-x+30\)
D \(x^2-30x+11\)
Explanation opens after your attempt
Correct Answer
B. \(x^2-11x+30\)
Step 1
Concept
The coefficient of (x) is (-6-5=-11) and the constant term is (30). Exam tip: product of two negative numbers is positive.
Step 2
Why this answer is correct
The correct answer is B. \(x^2-11x+30\). The coefficient of (x) is (-6-5=-11) and the constant term is (30). Exam tip: product of two negative numbers is positive.
Step 3
Exam Tip
(x) का गुणांक (-6-5=-11) और स्थिर पद (30) है। परीक्षा में दो ऋणात्मक संख्याओं का गुणन धनात्मक होता है।
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( (4p-3q)2 ) का सही प्रसार कौन सा है?
Which is the correct expansion of ( (4p-3q)2 )?
#minus square
#coefficients
#expansion
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A \(16p^2-12pq+9q^2\)
B \(16p^2+24pq+9q^2\)
C \(16p^2-24pq+9q^2\)
D \(4p^2-24pq+3q^2\)
Explanation opens after your attempt
Correct Answer
C. \(16p^2-24pq+9q^2\)
Step 1
Concept
The middle term is \(-2\cdot4p\cdot3q=-24pq\). Exam tip: check both coefficient squares and sign.
Step 2
Why this answer is correct
The correct answer is C. \(16p^2-24pq+9q^2\). The middle term is \(-2\cdot4p\cdot3q=-24pq\). Exam tip: check both coefficient squares and sign.
Step 3
Exam Tip
बीच का पद \(-2\cdot4p\cdot3q=-24pq\) है। परीक्षा में गुणांकों के वर्ग और चिन्ह दोनों देखें।
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\( 1005^2-995^2 \) का मान क्या है?
What is the value of \( 1005^2-995^2 \)?
#difference of squares
#numerical identity
#large numbers
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A (10000)
B (20000)
C (5000)
D (2000)
Explanation opens after your attempt
Correct Answer
B. (20000)
Step 1
Concept
Using (a-2 -b-2 =(a+b)(a-b)), we get \(2000\cdot10=20000\). Exam tip: directly find sum and difference.
Step 2
Why this answer is correct
The correct answer is B. (20000). Using (a-2 -b-2 =(a+b)(a-b)), we get \(2000\cdot10=20000\). Exam tip: directly find sum and difference.
Step 3
Exam Tip
(a-2 -b-2 =(a+b)(a-b)) से \(2000\cdot10=20000\) मिलता है। परीक्षा में सीधे योग और अंतर निकालें।
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( (x+5)2 -(x-5)2 ) का सरल रूप क्या है?
What is the simplified form of ( (x+5)2 -(x-5)2 )?
#identity simplification
#plus minus square
#4ab
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A (10x)
B (20)
C (20x)
D \(2x^2+50\)
Explanation opens after your attempt
Step 1
Concept
( (a+b)2 -(a-b)2 =4ab ). Here (a=x) and (b=5), so the result is (20x).
Step 2
Why this answer is correct
The correct answer is C. (20x). ( (a+b)2 -(a-b)2 =4ab ). Here (a=x) and (b=5), so the result is (20x).
Step 3
Exam Tip
( (a+b)2 -(a-b)2 =4ab ) है। यहाँ (a=x) और (b=5) इसलिए (20x) मिलेगा।
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( (x+5)2 +(x-5)2 ) का सरल रूप क्या है?
What is the simplified form of ( (x+5)2 +(x-5)2 )?
#sum identity
#plus minus square
#simplification
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A \(2x^2+10\)
B \(2x^2+50\)
C (20x)
D \(x^2+25\)
Explanation opens after your attempt
Correct Answer
B. \(2x^2+50\)
Step 1
Concept
( (a+b)2 +(a-b)2 =2a-2 +2b-2 ). Here it is \(2x^2+2\cdot25=2x^2+50\).
Step 2
Why this answer is correct
The correct answer is B. \(2x^2+50\). ( (a+b)2 +(a-b)2 =2a-2 +2b-2 ). Here it is \(2x^2+2\cdot25=2x^2+50\).
Step 3
Exam Tip
( (a+b)2 +(a-b)2 =2a-2 +2b-2 ) होता है। यहाँ \(2x^2+2\cdot25=2x^2+50\) है।
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\( 49^2 \) निकालने के लिए (49) को किस रूप में लिखना सबसे सरल है?
To calculate \(49^2\), writing (49) in which form is simplest?
#mental math
#49 square
#minus identity
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A (40+9)
B (48+1)
C (50-1)
D (45+4)
Explanation opens after your attempt
Step 1
Concept
Writing (49=50-1) makes use of ( (a-b)2 ) easy. Exam tip: take a nearby round number.
Step 2
Why this answer is correct
The correct answer is C. (50-1). Writing (49=50-1) makes use of ( (a-b)2 ) easy. Exam tip: take a nearby round number.
Step 3
Exam Tip
(49=50-1) लिखने से ( (a-b)2 ) का उपयोग आसान होता है। परीक्षा में नजदीकी गोल संख्या लें।
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( (2x+3y)2 -(2x-3y)2 ) का सरल रूप क्या है?
What is the simplified form of ( (2x+3y)2 -(2x-3y)2 )?
#identity simplification
#4ab
#two variables
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A (12xy)
B (24xy)
C \(4x^2-9y^2\)
D \(8x^2+18y^2\)
Explanation opens after your attempt
Step 1
Concept
This is ( (a+b)2 -(a-b)2 =4ab ), where (a=2x) and (b=3y). So it gives (24xy).
Step 2
Why this answer is correct
The correct answer is B. (24xy). This is ( (a+b)2 -(a-b)2 =4ab ), where (a=2x) and (b=3y). So it gives (24xy).
Step 3
Exam Tip
यह ( (a+b)2 -(a-b)2 =4ab ) है जहाँ (a=2x) और (b=3y) है। इसलिए (24xy) मिलता है।
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\( 73^2-27^2 \) का मान क्या है?
What is the value of \( 73^2-27^2 \)?
#numeric identity
#difference of squares
#shortcut
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A (4600)
B (5400)
C (4000)
D (5000)
Explanation opens after your attempt
Step 1
Concept
Using (a-2 -b-2 =(a+b)(a-b)), \(100\cdot46=4600\). Exam tip: do not calculate both squares separately.
Step 2
Why this answer is correct
The correct answer is A. (4600). Using (a-2 -b-2 =(a+b)(a-b)), \(100\cdot46=4600\). Exam tip: do not calculate both squares separately.
Step 3
Exam Tip
(a-2 -b-2 =(a+b)(a-b)) से \(100\cdot46=4600\) है। परीक्षा में बड़े वर्ग अलग-अलग न निकालें।
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( (3x+2)(3x+5) ) का प्रसार कौन सा है?
Which is the expansion of ( (3x+2)(3x+5) )?
#binomial product
#cross terms
#expansion
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A \(9x^2+7x+10\)
B \(9x^2+21x+10\)
C \(6x^2+21x+10\)
D \(9x^2+15x+10\)
Explanation opens after your attempt
Correct Answer
B. \(9x^2+21x+10\)
Step 1
Concept
\(3x\cdot5+2\cdot3x=15x+6x=21x\). Exam tip: add both cross terms.
Step 2
Why this answer is correct
The correct answer is B. \(9x^2+21x+10\). \(3x\cdot5+2\cdot3x=15x+6x=21x\). Exam tip: add both cross terms.
Step 3
Exam Tip
\(3x\cdot5+2\cdot3x=15x+6x=21x\) है। परीक्षा में दोनों क्रॉस पद जोड़ें।
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\( 2x^2+12x+18 \) को सरल गुणनखंड रूप में कौन सा लिखा जा सकता है?
Which can be written as the simplified factor form of \( 2x^2+12x+18 \)?
#factorisation
#common factor
#perfect square
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A (2(x+3)2 )
B (2(x+6)2 )
C ( (2x+3)2 )
D (2(x-3)2 )
Explanation opens after your attempt
Correct Answer
A. (2(x+3)2 )
Step 1
Concept
First take common (2), giving (2\(x^2+6x+9\)). The inside part is ( (x+3)2 ).
Step 2
Why this answer is correct
The correct answer is A. (2(x+3)2 ). First take common (2), giving (2\(x^2+6x+9\)). The inside part is ( (x+3)2 ).
Step 3
Exam Tip
पहले (2) सामान्य लें तो (2\(x^2+6x+9\)) मिलेगा। अंदर का भाग ( (x+3)2 ) है।
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\( 9a^2-25b^2 \) का गुणनखंड रूप क्या है?
What is the factor form of \( 9a^2-25b^2 \)?
#factorisation
#difference of squares
#two variables
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A ( (9a+25b)(a-b) )
B ( (3a-5b)2 )
C ( (3a+5b)(3a-5b) )
D ( (9a-25b)(a+b) )
Explanation opens after your attempt
Correct Answer
C. ( (3a+5b)(3a-5b) )
Step 1
Concept
(9a-2 =(3a)2 ) and (25b-2 =(5b)2 ). Therefore the difference of squares rule applies.
Step 2
Why this answer is correct
The correct answer is C. ( (3a+5b)(3a-5b) ). (9a-2 =(3a)2 ) and (25b-2 =(5b)2 ). Therefore the difference of squares rule applies.
Step 3
Exam Tip
(9a-2 =(3a)2 ) और (25b-2 =(5b)2 ) है। इसलिए अंतर के वर्गों का नियम लगेगा।
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( (a+b+c)2 ) में (ab) वाला पद किससे बनता है?
In ( (a+b+c)2 ), from where is the (ab)-term formed?
#three term identity
#ab term
#pair product
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A \(a^2+b^2\) से / From \(a^2+b^2\)
B (2ab) से / From (2ab)
C (abc) से / From (abc)
D \(b^2+c^2\) से / From \(b^2+c^2\)
Explanation opens after your attempt
Correct Answer
B. (2ab) से / From (2ab)
Step 1
Concept
In the square of three terms, twice the product of every pair appears. From (a) and (b), we get (2ab).
Step 2
Why this answer is correct
The correct answer is B. (2ab) से / From (2ab). In the square of three terms, twice the product of every pair appears. From (a) and (b), we get (2ab).
Step 3
Exam Tip
तीन पदों के वर्ग में हर दो पदों का दोगुना गुणनफल आता है। (a) और (b) से (2ab) मिलता है।
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( (2x+y+1)2 ) में स्थिर पद क्या है?
What is the constant term in ( (2x+y+1)2 )?
#constant term
#three term square
#identity
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A (2)
B (4)
C (1)
D (0)
Explanation opens after your attempt
Step 1
Concept
The constant term comes from \(1^2=1\). Exam tip: only the term without variables is the constant term.
Step 2
Why this answer is correct
The correct answer is C. (1). The constant term comes from \(1^2=1\). Exam tip: only the term without variables is the constant term.
Step 3
Exam Tip
स्थिर पद \(1^2=1\) से आता है। परीक्षा में केवल बिना चर वाले पद को स्थिर पद मानें।
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( (x+2)2 -\(x^2+4\) ) का सरल रूप क्या है?
What is the simplified form of ( (x+2)2 -\(x^2+4\) )?
#simplification
#square identity
#common error
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A (2x)
B (4x)
C \(x^2+4x\)
D (8x)
Explanation opens after your attempt
Step 1
Concept
( (x+2)2 =x-2 +4x+4 ). Subtracting \(x^2+4\) leaves (4x).
Step 2
Why this answer is correct
The correct answer is B. (4x). ( (x+2)2 =x-2 +4x+4 ). Subtracting \(x^2+4\) leaves (4x).
Step 3
Exam Tip
( (x+2)2 =x-2 +4x+4 ) है। \(x^2+4\) घटाने पर (4x) बचता है।
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( (3x-1)2 -\(9x^2+1\) ) का सरल रूप क्या है?
What is the simplified form of ( (3x-1)2 -\(9x^2+1\) )?
#simplification
#minus square
#linear term
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A (6x)
B (-6x)
C (18x)
D (-18x)
Explanation opens after your attempt
Step 1
Concept
( (3x-1)2 =9x-2 -6x+1 ). Subtracting \(9x^2+1\) leaves (-6x).
Step 2
Why this answer is correct
The correct answer is B. (-6x). ( (3x-1)2 =9x-2 -6x+1 ). Subtracting \(9x^2+1\) leaves (-6x).
Step 3
Exam Tip
( (3x-1)2 =9x-2 -6x+1 ) है। \(9x^2+1\) घटाने पर (-6x) बचता है।
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( (a+b)2 =a-2 +10ab+b-2 ) हो तो मानक सर्वसमिका के अनुसार बीच के पद में गलती क्या है?
If ( (a+b)2 =a-2 +10ab+b-2 ), what is the error in the middle term according to the standard identity?
#error spotting
#square identity
#middle term
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A बीच का पद (ab) होना चाहिए / The middle term should be (ab)
B बीच का पद (2ab) होना चाहिए / The middle term should be (2ab)
C बीच का पद (-2ab) होना चाहिए / The middle term should be (-2ab)
D कोई गलती नहीं है / There is no error
Explanation opens after your attempt
Correct Answer
B. बीच का पद (2ab) होना चाहिए / The middle term should be (2ab)
Step 1
Concept
The standard identity is ( (a+b)2 =a-2 +2ab+b-2 ). Exam tip: do not add an extra coefficient like (10ab).
Step 2
Why this answer is correct
The correct answer is B. बीच का पद (2ab) होना चाहिए / The middle term should be (2ab). The standard identity is ( (a+b)2 =a-2 +2ab+b-2 ). Exam tip: do not add an extra coefficient like (10ab).
Step 3
Exam Tip
मानक सर्वसमिका ( (a+b)2 =a-2 +2ab+b-2 ) है। परीक्षा में (10ab) जैसा अतिरिक्त गुणांक न लगाएँ।
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( (x-4)2 =x-2 -8x+16 ) में (-8x) कैसे आया?
How does (-8x) appear in ( (x-4)2 =x-2 -8x+16 )?
#middle term
#minus square
#identity reasoning
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A \(x\cdot4\) से / From \(x\cdot4\)
B \(4^2\) से / From \(4^2\)
C \(-2\cdot x\cdot4\) से / From \(-2\cdot x\cdot4\)
D \(x^2-4^2\) से / From \(x^2-4^2\)
Explanation opens after your attempt
Correct Answer
C. \(-2\cdot x\cdot4\) से / From \(-2\cdot x\cdot4\)
Step 1
Concept
In the minus square identity, the middle term is (-2ab). Here \(-2\cdot x\cdot4=-8x\).
Step 2
Why this answer is correct
The correct answer is C. \(-2\cdot x\cdot4\) से / From \(-2\cdot x\cdot4\). In the minus square identity, the middle term is (-2ab). Here \(-2\cdot x\cdot4=-8x\).
Step 3
Exam Tip
घटाव वाली वर्ग सर्वसमिका में बीच का पद (-2ab) होता है। यहाँ \(-2\cdot x\cdot4=-8x\) है।
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( (2a+b)2 +(2a-b)2 ) का सरल रूप क्या है?
What is the simplified form of ( (2a+b)2 +(2a-b)2 )?
#sum identity
#two variable
#simplification
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A \(8a^2+2b^2\)
B \(4a^2+2b^2\)
C \(8a^2+4b^2\)
D (4ab)
Explanation opens after your attempt
Correct Answer
A. \(8a^2+2b^2\)
Step 1
Concept
( (u+v)2 +(u-v)2 =2u-2 +2v-2 ). With (u=2a) and (v=b), the result is \(8a^2+2b^2\).
Step 2
Why this answer is correct
The correct answer is A. \(8a^2+2b^2\). ( (u+v)2 +(u-v)2 =2u-2 +2v-2 ). With (u=2a) and (v=b), the result is \(8a^2+2b^2\).
Step 3
Exam Tip
( (u+v)2 +(u-v)2 =2u-2 +2v-2 ) है। यहाँ (u=2a) और (v=b) रखने पर \(8a^2+2b^2\) मिलता है।
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( (5x+1)2 -(5x-1)2 ) का मान क्या है?
What is the value of ( (5x+1)2 -(5x-1)2 )?
#difference identity
#4uv
#simplification
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A (10x)
B (20x)
C \(25x^2-1\)
D (4x)
Explanation opens after your attempt
Step 1
Concept
( (u+v)2 -(u-v)2 =4uv ). Here (u=5x) and (v=1), so it is (20x).
Step 2
Why this answer is correct
The correct answer is B. (20x). ( (u+v)2 -(u-v)2 =4uv ). Here (u=5x) and (v=1), so it is (20x).
Step 3
Exam Tip
( (u+v)2 -(u-v)2 =4uv ) है। यहाँ (u=5x) और (v=1) इसलिए (20x) है।
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( (x+3)(x+7)-x-2 ) का सरल रूप क्या है?
What is the simplified form of ( (x+3)(x+7)-x-2 )?
#binomial product
#simplification
#linear expression
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A (10x+21)
B (21x+10)
C \(x^2+10x+21\)
D (10x-21)
Explanation opens after your attempt
Correct Answer
A. (10x+21)
Step 1
Concept
( (x+3)(x+7)=x-2 +10x+21 ). Subtracting \(x^2\) leaves (10x+21).
Step 2
Why this answer is correct
The correct answer is A. (10x+21). ( (x+3)(x+7)=x-2 +10x+21 ). Subtracting \(x^2\) leaves (10x+21).
Step 3
Exam Tip
( (x+3)(x+7)=x-2 +10x+21 ) है। \(x^2\) घटाने पर (10x+21) बचता है।
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( (x-2)(x+9)-x-2 ) का सरल रूप क्या है?
What is the simplified form of ( (x-2)(x+9)-x-2 )?
#binomial product
#mixed signs
#simplification
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A (11x-18)
B (7x-18)
C (7x+18)
D (-7x-18)
Explanation opens after your attempt
Correct Answer
B. (7x-18)
Step 1
Concept
( (x-2)(x+9)=x-2 +7x-18 ). Subtracting \(x^2\) gives (7x-18).
Step 2
Why this answer is correct
The correct answer is B. (7x-18). ( (x-2)(x+9)=x-2 +7x-18 ). Subtracting \(x^2\) gives (7x-18).
Step 3
Exam Tip
( (x-2)(x+9)=x-2 +7x-18 ) है। \(x^2\) घटाने पर (7x-18) मिलता है।
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( (a+b)2 -\(a^2+b^2\) ) का मान क्या है?
What is the value of ( (a+b)2 -\(a^2+b^2\) )?
#identity difference
#common mistake
#2ab
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A (ab)
B \(a^2-b^2\)
C (2ab)
D (4ab)
Explanation opens after your attempt
Step 1
Concept
( (a+b)2 =a-2 +2ab+b-2 ). Subtracting \(a^2+b^2\) leaves (2ab).
Step 2
Why this answer is correct
The correct answer is C. (2ab). ( (a+b)2 =a-2 +2ab+b-2 ). Subtracting \(a^2+b^2\) leaves (2ab).
Step 3
Exam Tip
( (a+b)2 =a-2 +2ab+b-2 ) है। \(a^2+b^2\) घटाने पर (2ab) बचता है।
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( (a-b)2 -\(a^2+b^2\) ) का सरल रूप क्या है?
What is the simplified form of ( (a-b)2 -\(a^2+b^2\) )?
#minus square
#simplification
#negative middle term
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A (2ab)
B \(a^2-b^2\)
C (-2ab)
D (0)
Explanation opens after your attempt
Step 1
Concept
( (a-b)2 =a-2 -2ab+b-2 ). Subtracting \(a^2+b^2\) leaves (-2ab).
Step 2
Why this answer is correct
The correct answer is C. (-2ab). ( (a-b)2 =a-2 -2ab+b-2 ). Subtracting \(a^2+b^2\) leaves (-2ab).
Step 3
Exam Tip
( (a-b)2 =a-2 -2ab+b-2 ) है। \(a^2+b^2\) घटाने पर (-2ab) बचता है।
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( (2x+5)2 -25 ) का सरल गुणनखंड रूप क्या है?
What is the simplified factor form of ( (2x+5)2 -25 )?
#factorisation
#difference of squares
#simplified form
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A (4x(x+5))
B (2x(2x+10))
C \(4x^2+20x\)
D ( (2x+5)(2x-5) )
Explanation opens after your attempt
Correct Answer
A. (4x(x+5))
Step 1
Concept
First treat ( (2x+5)2 -52 ) as \(a^2-b^2\). Then ( (2x)(2x+10)=4x(x+5) ).
Step 2
Why this answer is correct
The correct answer is A. (4x(x+5)). First treat ( (2x+5)2 -52 ) as \(a^2-b^2\). Then ( (2x)(2x+10)=4x(x+5) ).
Step 3
Exam Tip
पहले ( (2x+5)2 -52 ) को \(a^2-b^2\) मानें। फिर ( (2x)(2x+10)=4x(x+5) ) मिलता है।
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\( 4x^2+12x+9 \) किसका वर्ग है?
\( 4x^2+12x+9 \) is the square of what?
#perfect square
#recognition
#2x plus 3
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A ( (4x+3)2 )
B ( (2x+3)2 )
C ( (2x-3)2 )
D ( (x+3)2 )
Explanation opens after your attempt
Correct Answer
B. ( (2x+3)2 )
Step 1
Concept
(4x-2 =(2x)2 ) and \(9=3^2\). The middle term is \(2\cdot2x\cdot3=12x\).
Step 2
Why this answer is correct
The correct answer is B. ( (2x+3)2 ). (4x-2 =(2x)2 ) and \(9=3^2\). The middle term is \(2\cdot2x\cdot3=12x\).
Step 3
Exam Tip
(4x-2 =(2x)2 ) और \(9=3^2\) है। बीच का पद \(2\cdot2x\cdot3=12x\) है।
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\( 16y^2-40y+25 \) किसका वर्ग है?
\( 16y^2-40y+25 \) is the square of what?
#perfect square
#minus identity
#recognition
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A ( (4y+5)2 )
B ( (16y-5)2 )
C ( (4y-5)2 )
D ( (2y-5)2 )
Explanation opens after your attempt
Correct Answer
C. ( (4y-5)2 )
Step 1
Concept
(16y-2 =(4y)2 ) and \(25=5^2\). The negative middle term makes it ( (4y-5)2 ).
Step 2
Why this answer is correct
The correct answer is C. ( (4y-5)2 ). (16y-2 =(4y)2 ) and \(25=5^2\). The negative middle term makes it ( (4y-5)2 ).
Step 3
Exam Tip
(16y-2 =(4y)2 ) और \(25=5^2\) है। ऋणात्मक बीच का पद इसे ( (4y-5)2 ) बनाता है।
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( (x+a)(x+b) ) का सामान्य प्रसार कौन सा है?
What is the general expansion of ( (x+a)(x+b) )?
#general identity
#x plus a
#x plus b
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A \(x^2+abx+a+b\)
B (x-2 +(a-b)x+ab)
C \(x^2+ab\)
D (x-2 +(a+b)x+ab)
Explanation opens after your attempt
Correct Answer
D. (x-2 +(a+b)x+ab)
Step 1
Concept
The two cross terms (ax) and (bx) combine to form ((a+b)x). Exam tip: remember the constant term (ab).
Step 2
Why this answer is correct
The correct answer is D. (x-2 +(a+b)x+ab). The two cross terms (ax) and (bx) combine to form ((a+b)x). Exam tip: remember the constant term (ab).
Step 3
Exam Tip
दो क्रॉस पद (ax) और (bx) मिलकर ((a+b)x) बनाते हैं। परीक्षा में स्थिर पद (ab) याद रखें।
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( (2x+1)(2x+7) ) में (x) का गुणांक क्या है?
What is the coefficient of (x) in ( (2x+1)(2x+7) )?
#coefficient
#cross terms
#binomial product
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A (16)
B (14)
C (8)
D (4)
Explanation opens after your attempt
Step 1
Concept
The cross terms are \(2x\cdot7=14x\) and \(1\cdot2x=2x\). Total is (16x).
Step 2
Why this answer is correct
The correct answer is A. (16). The cross terms are \(2x\cdot7=14x\) and \(1\cdot2x=2x\). Total is (16x).
Step 3
Exam Tip
क्रॉस पद \(2x\cdot7=14x\) और \(1\cdot2x=2x\) हैं। कुल (16x) है।
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( (3a-2)(3a+8) ) में (a) का गुणांक क्या है?
What is the coefficient of (a) in ( (3a-2)(3a+8) )?
#coefficient
#mixed signs
#binomial product
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A (18)
B (24)
C (12)
D (6)
Explanation opens after your attempt
Step 1
Concept
The cross terms are \(3a\cdot8=24a\) and \(-2\cdot3a=-6a\). Total is (18a).
Step 2
Why this answer is correct
The correct answer is A. (18). The cross terms are \(3a\cdot8=24a\) and \(-2\cdot3a=-6a\). Total is (18a).
Step 3
Exam Tip
क्रॉस पद \(3a\cdot8=24a\) और \(-2\cdot3a=-6a\) हैं। कुल (18a) है।
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( (a+b+c)2 -\(a^2+b^2+c^2\) ) का सरल रूप क्या है?
What is the simplified form of ( (a+b+c)2 -\(a^2+b^2+c^2\) )?
#three term square
#simplification
#pair terms
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A (ab+bc+ca)
B (2ab+2bc+2ca)
C (3abc)
D (a+b+c)
Explanation opens after your attempt
Correct Answer
B. (2ab+2bc+2ca)
Step 1
Concept
After removing square terms from the three-term square, (2ab+2bc+2ca) remains. Exam tip: remember pairwise terms.
Step 2
Why this answer is correct
The correct answer is B. (2ab+2bc+2ca). After removing square terms from the three-term square, (2ab+2bc+2ca) remains. Exam tip: remember pairwise terms.
Step 3
Exam Tip
तीन पदों के वर्ग से वर्ग पद हटाने पर (2ab+2bc+2ca) बचता है। परीक्षा में जोड़ीदार पद याद रखें।
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( (x+2y-3z)2 ) में (xz) वाला पद क्या है?
What is the (xz)-term in ( (x+2y-3z)2 )?
#xz term
#three term square
#negative coefficient
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A (6xz)
B (-6xz)
C (-3xz)
D (3xz)
Explanation opens after your attempt
Step 1
Concept
From (x) and (-3z), (2\cdot x\cdot(-3z)=-6xz). Exam tip: apply the sign carefully.
Step 2
Why this answer is correct
The correct answer is B. (-6xz). From (x) and (-3z), (2\cdot x\cdot(-3z)=-6xz). Exam tip: apply the sign carefully.
Step 3
Exam Tip
(x) और (-3z) से (2\cdot x\cdot(-3z)=-6xz) मिलता है। परीक्षा में चिन्ह ध्यान से लगाएँ।
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( (2p-3q+r)2 ) में (pq) वाला पद क्या होगा?
What will be the (pq)-term in ( (2p-3q+r)2 )?
#pq term
#three term square
#signs
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A (6pq)
B (-3pq)
C (-12pq)
D (12pq)
Explanation opens after your attempt
Correct Answer
C. (-12pq)
Step 1
Concept
Twice the product of (2p) and (-3q) is (2\cdot2p\cdot(-3q)=-12pq). Exam tip: check both pair and sign.
Step 2
Why this answer is correct
The correct answer is C. (-12pq). Twice the product of (2p) and (-3q) is (2\cdot2p\cdot(-3q)=-12pq). Exam tip: check both pair and sign.
Step 3
Exam Tip
(2p) और (-3q) का दोगुना गुणनफल (2\cdot2p\cdot(-3q)=-12pq) है। परीक्षा में जोड़े और चिन्ह दोनों देखें।
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\( 64x^2-1 \) का गुणनखंड रूप क्या है?
What is the factor form of \( 64x^2-1 \)?
#factorisation
#difference of squares
#64x square
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A ( (8x+1)(8x-1) )
B ( (64x+1)(x-1) )
C ( (8x-1)2 )
D ( (4x+1)(4x-1) )
Explanation opens after your attempt
Correct Answer
A. ( (8x+1)(8x-1) )
Step 1
Concept
(64x-2 =(8x)2 ) and \(1=1^2\). Therefore the rule \(a^2-b^2\) applies.
Step 2
Why this answer is correct
The correct answer is A. ( (8x+1)(8x-1) ). (64x-2 =(8x)2 ) and \(1=1^2\). Therefore the rule \(a^2-b^2\) applies.
Step 3
Exam Tip
(64x-2 =(8x)2 ) और \(1=1^2\) है। इसलिए \(a^2-b^2\) का नियम लगेगा।
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\( 121-4y^2 \) का सही गुणनखंड रूप कौन सा है?
Which is the correct factor form of \( 121-4y^2 \)?
#factorisation
#difference of squares
#121
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A ( (11-2y)2 )
B ( (11+2y)(11-2y) )
C ( (121+2y)(1-2y) )
D ( (11+y)(11-y) )
Explanation opens after your attempt
Correct Answer
B. ( (11+2y)(11-2y) )
Step 1
Concept
\(121=11^2\) and (4y-2 =(2y)2 ). Difference of squares gives ( (11+2y)(11-2y) ).
Step 2
Why this answer is correct
The correct answer is B. ( (11+2y)(11-2y) ). \(121=11^2\) and (4y-2 =(2y)2 ). Difference of squares gives ( (11+2y)(11-2y) ).
Step 3
Exam Tip
\(121=11^2\) और (4y-2 =(2y)2 ) है। अंतर के वर्गों से ( (11+2y)(11-2y) ) मिलेगा।
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( (x+6)(x-6)+36 ) का सरल रूप क्या है?
What is the simplified form of ( (x+6)(x-6)+36 )?
#difference of squares
#simplification
#product identity
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A \(x^2-72\)
B \(x^2+72\)
C \(x^2\)
D \(x^2+36\)
Explanation opens after your attempt
Correct Answer
C. \(x^2\)
Step 1
Concept
( (x+6)(x-6)=x-2 -36 ). Adding (36) leaves \(x^2\).
Step 2
Why this answer is correct
The correct answer is C. \(x^2\). ( (x+6)(x-6)=x-2 -36 ). Adding (36) leaves \(x^2\).
Step 3
Exam Tip
( (x+6)(x-6)=x-2 -36 ) है। फिर (36) जोड़ने पर \(x^2\) बचता है।
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( (3x+4)2 -(3x-4)2 ) का सरल रूप क्या है?
What is the simplified form of ( (3x+4)2 -(3x-4)2 )?
#identity simplification
#4uv
#3x plus minus 4
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A (48x)
B (24x)
C (12x)
D \(9x^2-16\)
Explanation opens after your attempt
Step 1
Concept
( (u+v)2 -(u-v)2 =4uv ). Here (u=3x) and (v=4), so the result is (48x).
Step 2
Why this answer is correct
The correct answer is A. (48x). ( (u+v)2 -(u-v)2 =4uv ). Here (u=3x) and (v=4), so the result is (48x).
Step 3
Exam Tip
( (u+v)2 -(u-v)2 =4uv ) है। यहाँ (u=3x) और (v=4) इसलिए (48x) मिलेगा।
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( (x+1)(x+2)(x+3) ) को पहले दो गुणनखंडों से शुरू करने पर कौन सा मध्य रूप सही है?
When starting ( (x+1)(x+2)(x+3) ) with the first two factors, which intermediate form is correct?
#binomial product
#intermediate form
#stepwise expansion
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A ( \(x^2+3x+2\)(x+3) )
B ( \(x^2+2x+3\)(x+3) )
C ( \(x^2+5x+2\)(x+3) )
D ( \(x^2+3x-2\)(x+3) )
Explanation opens after your attempt
Correct Answer
A. ( \(x^2+3x+2\)(x+3) )
Step 1
Concept
First ( (x+1)(x+2)=x-2 +3x+2 ). Exam tip: keep small steps correct.
Step 2
Why this answer is correct
The correct answer is A. ( \(x^2+3x+2\)(x+3) ). First ( (x+1)(x+2)=x-2 +3x+2 ). Exam tip: keep small steps correct.
Step 3
Exam Tip
पहले ( (x+1)(x+2)=x-2 +3x+2 ) है। परीक्षा में छोटे चरण सही रखें।
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( (2x-3)(2x+9) ) में (x) का गुणांक क्या होगा?
What will be the coefficient of (x) in ( (2x-3)(2x+9) )?
#coefficient
#cross terms
#binomial product
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A (12)
B (18)
C (6)
D (-6)
Explanation opens after your attempt
Step 1
Concept
The cross terms are \(2x\cdot9=18x\) and \(-3\cdot2x=-6x\). Total is (12x).
Step 2
Why this answer is correct
The correct answer is A. (12). The cross terms are \(2x\cdot9=18x\) and \(-3\cdot2x=-6x\). Total is (12x).
Step 3
Exam Tip
क्रॉस पद \(2x\cdot9=18x\) और \(-3\cdot2x=-6x\) हैं। कुल (12x) है।
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( (x-5)(x+11) ) का प्रसार करने पर (x) का गुणांक क्या होगा?
What will be the coefficient of (x) after expanding ( (x-5)(x+11) )?
#coefficient
#binomial product
#algebraic identities
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A (6)
B (16)
C (-55)
D (-6)
Explanation opens after your attempt
Step 1
Concept
The cross terms are (11x) and (-5x), so the total is (6x). Exam tip: take the algebraic sum of numbers for the coefficient of (x).
Step 2
Why this answer is correct
The correct answer is A. (6). The cross terms are (11x) and (-5x), so the total is (6x). Exam tip: take the algebraic sum of numbers for the coefficient of (x).
Step 3
Exam Tip
क्रॉस पद (11x) और (-5x) हैं, इसलिए कुल (6x) मिलता है। परीक्षा में (x) के गुणांक के लिए संख्याओं का बीजगणितीय योग करें।
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