\(x^2+bx+25\) पूर्ण वर्ग हो और (b) ऋणात्मक हो, तो (b) क्या होगा?
If \(x^2+bx+25\) is a perfect square and (b) is negative, what is (b)?
#quadratic expressions
#missing coefficient
#minus square
A (10)
B (-10)
C (5)
D (-5)
Explanation opens after your attempt
Step 1
Concept
Since \(25=5^2\), for the negative perfect square \(b=-2\cdot5=-10\). Exam tip: read the sign condition carefully.
Step 2
Why this answer is correct
The correct answer is B. (-10). Since \(25=5^2\), for the negative perfect square \(b=-2\cdot5=-10\). Exam tip: read the sign condition carefully.
Step 3
Exam Tip
\(25=5^2\), इसलिए ऋणात्मक पूर्ण वर्ग में \(b=-2\cdot5=-10\) है। परीक्षा में संकेत शर्त जरूर पढ़ें।
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\(x^2-14x+49\) किस पूर्ण वर्ग के बराबर है?
Which perfect square equals \(x^2-14x+49\)?
#quadratic expressions
#perfect square
#minus square
A ((x+7)2 )
B ((x-14)2 )
C ((x+14)2 )
D ((x-7)2 )
Explanation opens after your attempt
Correct Answer
D. ((x-7)2 )
Step 1
Concept
Here \(49=7^2\) and \(-14x=-2\cdot7\cdot x\). Exam tip: identify ((x-7)2 ) from the negative middle term.
Step 2
Why this answer is correct
The correct answer is D. ((x-7)2 ). Here \(49=7^2\) and \(-14x=-2\cdot7\cdot x\). Exam tip: identify ((x-7)2 ) from the negative middle term.
Step 3
Exam Tip
\(49=7^2\) और \(-14x=-2\cdot7\cdot x\) है। परीक्षा में ऋणात्मक मध्य पद से ((x-7)2 ) पहचानें।
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((x-5)2 ) का सही विस्तार क्या है?
What is the correct expansion of ((x-5)2 )?
#quadratic expressions
#minus square
#expansion
A \(x^2-5x+25\)
B \(x^2-10x+25\)
C \(x^2+10x+25\)
D \(x^2-25\)
Explanation opens after your attempt
Correct Answer
B. \(x^2-10x+25\)
Step 1
Concept
((x-5)2 =x-2 -2\cdot x\cdot5+25). Exam tip: note both the negative sign and (2ab).
Step 2
Why this answer is correct
The correct answer is B. \(x^2-10x+25\). ((x-5)2 =x-2 -2\cdot x\cdot5+25). Exam tip: note both the negative sign and (2ab).
Step 3
Exam Tip
((x-5)2 =x-2 -2\cdot x\cdot5+25) है। परीक्षा में ऋण चिन्ह और (2ab) दोनों ध्यान रखें।
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\(a^2-2ab+b^2\) किसके बराबर है?
What is \(a^2-2ab+b^2\) equal to?
#minus square
#quadratic identity
#factor form
A ((a+b)2 )
B ((a-b)2 )
C \(a^2-b^2\)
D (2ab)
Explanation opens after your attempt
Correct Answer
B. ((a-b)2 )
Step 1
Concept
The middle term is negative, so it is a subtraction perfect square. The correct form is ((a-b)2 ).
Step 2
Why this answer is correct
The correct answer is B. ((a-b)2 ). The middle term is negative, so it is a subtraction perfect square. The correct form is ((a-b)2 ).
Step 3
Exam Tip
मध्य पद ऋण है इसलिए यह घटाव वाला पूर्ण वर्ग है। सही रूप ((a-b)2 ) है।
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((x-4)2 ) का विस्तार क्या है?
What is the expansion of ((x-4)2 )?
#minus square
#expansion
#quadratic
A \(x^2-4x+16\)
B \(x^2+8x+16\)
C \(x^2-8x+16\)
D \(x^2-16\)
Explanation opens after your attempt
Correct Answer
C. \(x^2-8x+16\)
Step 1
Concept
((x-4)2 =x-2 -2\cdot x\cdot4+16). So \(x^2-8x+16\) is correct.
Step 2
Why this answer is correct
The correct answer is C. \(x^2-8x+16\). ((x-4)2 =x-2 -2\cdot x\cdot4+16). So \(x^2-8x+16\) is correct.
Step 3
Exam Tip
((x-4)2 =x-2 -2\cdot x\cdot4+16) है। इसलिए \(x^2-8x+16\) सही है।
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\(x^2-14x+49\) का सही गुणनखंड रूप क्या है?
What is the correct factorised form of \(x^2-14x+49\)?
#perfect square
#minus square
#factorisation
A ((x+7)2 )
B ((x-7)2 )
C ((x-14)(x+49))
D ((x-49)2 )
Explanation opens after your attempt
Correct Answer
B. ((x-7)2 )
Step 1
Concept
\(49=7^2\) and \(-14x=-2\times7\times x\). Exam tip: identify ((a-b)2 ) from the negative middle term.
Step 2
Why this answer is correct
The correct answer is B. ((x-7)2 ). \(49=7^2\) and \(-14x=-2\times7\times x\). Exam tip: identify ((a-b)2 ) from the negative middle term.
Step 3
Exam Tip
\(49=7^2\) और \(-14x=-2\times7\times x\) है। परीक्षा में ऋणात्मक मध्य पद देखकर ((a-b)2 ) पहचानें।
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\(z^2-4z+4\) का गुणनखंड रूप क्या है?
What is the factorised form of \(z^2-4z+4\)?
#minus square
#perfect square
#factorisation
A ((z+2)2 )
B (z(z-4)+4)
C ((z-2)2 )
D ((z-4)(z+1))
Explanation opens after your attempt
Correct Answer
C. ((z-2)2 )
Step 1
Concept
\(4=2^2\) and \(-4z=-2\times z\times2\), so it is ((z-2)2 ). Exam tip: identify subtraction perfect squares.
Step 2
Why this answer is correct
The correct answer is C. ((z-2)2 ). \(4=2^2\) and \(-4z=-2\times z\times2\), so it is ((z-2)2 ). Exam tip: identify subtraction perfect squares.
Step 3
Exam Tip
\(4=2^2\) और \(-4z=-2\times z\times2\), इसलिए ((z-2)2 ) है। परीक्षा में घटाव वाले पूर्ण वर्ग को पहचानें।
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\(x^2-6x+9\) किसका वर्ग है?
Whose square is \(x^2-6x+9\)?
#minus square
#perfect square
#factorisation
A ((x-3)2 )
B ((x+3)2 )
C ((x-6)2 )
D ((x+9)2 )
Explanation opens after your attempt
Correct Answer
A. ((x-3)2 )
Step 1
Concept
Since \(9=3^2\) and the middle term is (-6x), the form is ((x-3)2 ). Exam tip: watch the negative sign.
Step 2
Why this answer is correct
The correct answer is A. ((x-3)2 ). Since \(9=3^2\) and the middle term is (-6x), the form is ((x-3)2 ). Exam tip: watch the negative sign.
Step 3
Exam Tip
\(9=3^2\) और बीच का पद (-6x) है, इसलिए रूप ((x-3)2 ) है। परीक्षा में ऋण चिह्न ध्यान से देखें।
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\(4x^2-12x+9\) के गुणनखंड क्या होंगे?
What are the factors of \(4x^2-12x+9\)?
#perfect-square
#minus-square
#factorisation
A ((2x+3)2 )
B ((2x-3)2 )
C ((4x-9)(x-1))
D ((2x-3)(2x+3))
Explanation opens after your attempt
Correct Answer
B. ((2x-3)2 )
Step 1
Concept
This is the perfect square of the difference of (2x) and (3). In exams, check \(-12x=-2\cdot2x\cdot3\).
Step 2
Why this answer is correct
The correct answer is B. ((2x-3)2 ). This is the perfect square of the difference of (2x) and (3). In exams, check \(-12x=-2\cdot2x\cdot3\).
Step 3
Exam Tip
यह (2x) और (3) के अंतर का पूर्ण वर्ग है। परीक्षा में \(-12x=-2\cdot2x\cdot3\) देखें।
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\(x^2-2xy+y^2\) को गुणनखंडित कीजिए।
Factorise \(x^2-2xy+y^2\).
#perfect-square
#minus-square
#two-variables
A ((x+y)2 )
B ((x-y)2 )
C ((x-y)(x+y))
D (y(x-y))
Explanation opens after your attempt
Correct Answer
B. ((x-y)2 )
Step 1
Concept
This is the perfect square of the difference of (x) and (y). In exams, identify ((x-y)2 ) from the negative middle term.
Step 2
Why this answer is correct
The correct answer is B. ((x-y)2 ). This is the perfect square of the difference of (x) and (y). In exams, identify ((x-y)2 ) from the negative middle term.
Step 3
Exam Tip
यह (x) और (y) के अंतर का पूर्ण वर्ग है। परीक्षा में ऋणात्मक मध्य पद से ((x-y)2 ) पहचानें।
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\(p^2-12p+36\) का सही गुणनखंड चुनिए।
Choose the correct factorisation of \(p^2-12p+36\).
#perfect-square
#minus-square
#factorisation
A ((p+6)2 )
B ((p-6)2 )
C ((p-12)(p+3))
D ((p-3)(p-12))
Explanation opens after your attempt
Correct Answer
B. ((p-6)2 )
Step 1
Concept
\(36=6^2\) and the middle term is negative. In exams, use the sign to choose ((p-6)2 ).
Step 2
Why this answer is correct
The correct answer is B. ((p-6)2 ). \(36=6^2\) and the middle term is negative. In exams, use the sign to choose ((p-6)2 ).
Step 3
Exam Tip
\(36=6^2\) और मध्य पद ऋणात्मक है। परीक्षा में चिह्न देखकर ((p-6)2 ) चुनें।
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\(y^2-10y+25\) का गुणनखंडन कौन सा है?
Which is the factorisation of \(y^2-10y+25\)?
#minus square
#perfect square
#factorisation
A ((y+5)2 )
B ((y-10)2 )
C ((y-5)2 )
D ((y-25)2 )
Explanation opens after your attempt
Correct Answer
C. ((y-5)2 )
Step 1
Concept
\(25=5^2\) and \(-10y=-2\cdot5y\). So (y-2 -10y+25=(y-5)2 ).
Step 2
Why this answer is correct
The correct answer is C. ((y-5)2 ). \(25=5^2\) and \(-10y=-2\cdot5y\). So (y-2 -10y+25=(y-5)2 ).
Step 3
Exam Tip
\(25=5^2\) और \(-10y=-2\cdot5y\) है। इसलिए (y-2 -10y+25=(y-5)2 ) है।
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यदि (2a-b) भुजा वाले वर्ग का दृश्य मॉडल बने, तो विस्तार क्या होगा?
If a visual model is made for a square of side (2a-b), what will be the expansion?
#minus-square
#coefficients
#visual
A \(4a^2-4ab+b^2\)
B \(4a^2-2ab+b^2\)
C \(2a^2-4ab+b^2\)
D \(4a^2+4ab+b^2\)
Explanation opens after your attempt
Correct Answer
A. \(4a^2-4ab+b^2\)
Step 1
Concept
The subtracted middle term is \(2\cdot2a\cdot b=4ab\). In exams, keep both the negative sign and coefficient.
Step 2
Why this answer is correct
The correct answer is A. \(4a^2-4ab+b^2\). The subtracted middle term is \(2\cdot2a\cdot b=4ab\). In exams, keep both the negative sign and coefficient.
Step 3
Exam Tip
बीच का घटा पद \(2\cdot2a\cdot b=4ab\) है। परीक्षा में ऋण चिह्न और गुणांक दोनों रखें।
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यदि (q-4) भुजा वाले वर्ग का अंतिम क्षेत्रफल चाहिए, तो सही विस्तार कौन-सा होगा?
If the final area of a square of side (q-4) is needed, which expansion is correct?
#minus-square
#visual-expansion
#identity
A \(q^2-4q+16\)
B \(q^2+8q+16\)
C \(q^2-8q+16\)
D \(q^2-16q+8\)
Explanation opens after your attempt
Correct Answer
C. \(q^2-8q+16\)
Step 1
Concept
The middle term is \(-2\cdot q\cdot4=-8q\). In exams, count (4) in two strips.
Step 2
Why this answer is correct
The correct answer is C. \(q^2-8q+16\). The middle term is \(-2\cdot q\cdot4=-8q\). In exams, count (4) in two strips.
Step 3
Exam Tip
बीच का पद \(-2\cdot q\cdot4=-8q\) है। परीक्षा में (4) को दो पट्टियों में गिनें।
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(n-5) भुजा वाले वर्ग में हटाई गई दो पट्टियों का कुल क्षेत्रफल क्या है?
In a square of side (n-5), what is the total area of the two removed strips?
#removed-strips
#minus-square
#visual
A (5n)
B (10n)
C (25n)
D (25)
Explanation opens after your attempt
Step 1
Concept
The two strips are (5n) and (5n), so total (10n) is removed. In exams, add both removed parts.
Step 2
Why this answer is correct
The correct answer is B. (10n). The two strips are (5n) and (5n), so total (10n) is removed. In exams, add both removed parts.
Step 3
Exam Tip
दो पट्टियाँ (5n) और (5n) हैं इसलिए कुल (10n) घटता है। परीक्षा में दोनों हटे भाग जोड़ें।
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यदि भुजा (a-b) वाले वर्ग का क्षेत्र \(a^2-2ab+b^2\) है, तो \(b^2\) का चिन्ह कैसा होगा?
If the area of a square with side (a-b) is \(a^2-2ab+b^2\), what will be the sign of \(b^2\)?
#signs
#minus-square
#visual-identity
A ऋणात्मक / Negative
B शून्य / Zero
C धनात्मक / Positive
D बदलता हुआ / Changing
Explanation opens after your attempt
Correct Answer
C. धनात्मक / Positive
Step 1
Concept
Because (b) is squared, \(b^2\) remains positive. Exam tip: only the middle term is negative.
Step 2
Why this answer is correct
The correct answer is C. धनात्मक / Positive. Because (b) is squared, \(b^2\) remains positive. Exam tip: only the middle term is negative.
Step 3
Exam Tip
(b) का वर्ग बनने से \(b^2\) धनात्मक रहता है। परीक्षा में केवल बीच का पद ऋणात्मक होता है।
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दृश्य मॉडल में \(x^2-10x+25\) किस वर्ग की भुजा को दिखाता है?
In a visual model, \(x^2-10x+25\) shows the side of which square?
#minus-square
#side-recognition
#visual-model
A (x+5)
B (x-10)
C (x-5)
D (x+25)
Explanation opens after your attempt
Step 1
Concept
Since \(25=5^2\) and \(-10x=-2\times x\times5\), the side is (x-5). Exam tip: look at the negative middle term.
Step 2
Why this answer is correct
The correct answer is C. (x-5). Since \(25=5^2\) and \(-10x=-2\times x\times5\), the side is (x-5). Exam tip: look at the negative middle term.
Step 3
Exam Tip
\(25=5^2\) और \(-10x=-2\times x\times5\), इसलिए भुजा (x-5) है। परीक्षा में ऋणात्मक बीच का पद देखें।
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भुजा (x-5) वाले वर्ग के मॉडल में अंतिम छोटा वर्ग किस क्षेत्र का होगा?
In the model of a square with side (x-5), what will be the area of the final small square?
#small-square
#minus-square
#visual-identity
A (5x)
B (10x)
C (25)
D \(x^2\)
Explanation opens after your attempt
Step 1
Concept
The small square has side (5), so its area is (25). Exam tip: the square of the negative part is positive.
Step 2
Why this answer is correct
The correct answer is C. (25). The small square has side (5), so its area is (25). Exam tip: the square of the negative part is positive.
Step 3
Exam Tip
छोटे वर्ग की भुजा (5) है इसलिए उसका क्षेत्र (25) है। परीक्षा में ऋणात्मक भाग का वर्ग धनात्मक होता है।
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भुजा (y-3) वाले वर्ग के क्षेत्र मॉडल में सही विस्तार कौन सा है?
Which expansion is correct in the area model of a square with side (y-3)?
#minus-square
#area-model
#identity
A \(y^2+6y+9\)
B \(y^2-3y+9\)
C \(y^2-6y+9\)
D \(y^2-9y+6\)
Explanation opens after your attempt
Correct Answer
C. \(y^2-6y+9\)
Step 1
Concept
Two (3y) strips are subtracted, and (9) is added back. Exam tip: keep the middle term negative in ((a-b)2 ).
Step 2
Why this answer is correct
The correct answer is C. \(y^2-6y+9\). Two (3y) strips are subtracted, and (9) is added back. Exam tip: keep the middle term negative in ((a-b)2 ).
Step 3
Exam Tip
दो (3y) पट्टियां घटती हैं और (9) वापस जुड़ता है। परीक्षा में ((a-b)2 ) में बीच का पद ऋणात्मक रखें।
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किस दृश्य मॉडल में पूरा क्षेत्रफल \(x^2-4x+4\) मिलता है?
Which visual model gives the whole area \(x^2-4x+4\)?
#minus square
#visual identification
#area model
A भुजा (x+2) का वर्ग / Square of side (x+2)
B भुजा (x-2) का वर्ग / Square of side (x-2)
C भुजा (x+4) का वर्ग / Square of side (x+4)
D लंबाई (x+2) और चौड़ाई (x-2) का आयत / Rectangle of length (x+2) and breadth (x-2)
Explanation opens after your attempt
Correct Answer
B. भुजा (x-2) का वर्ग / Square of side (x-2)
Step 1
Concept
(x-2 -4x+4=(x-2)2 ). Exam tip: identify the subtraction square from the negative middle term.
Step 2
Why this answer is correct
The correct answer is B. भुजा (x-2) का वर्ग / Square of side (x-2). (x-2 -4x+4=(x-2)2 ). Exam tip: identify the subtraction square from the negative middle term.
Step 3
Exam Tip
(x-2 -4x+4=(x-2)2 ) है। परीक्षा में ऋण मध्य पद देखकर घटाव वाला वर्ग पहचानें।
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यदि \(18^2\) को ((20-2)2 ) से निकालें तो अंत में जोड़ा जाने वाला छोटा वर्ग कितना है?
If \(18^2\) is found using ((20-2)2 ), what is the small square added at the end?
#minus square
#numeric model
#small area
A (2)
B (4)
C (40)
D (80)
Explanation opens after your attempt
Step 1
Concept
In ((20-2)2 ), the small square is \(2^2=4\). Exam tip: after subtracting two rectangles, add the small square.
Step 2
Why this answer is correct
The correct answer is B. (4). In ((20-2)2 ), the small square is \(2^2=4\). Exam tip: after subtracting two rectangles, add the small square.
Step 3
Exam Tip
((20-2)2 ) में छोटा वर्ग \(2^2=4\) है। परीक्षा में दो आयत घटाने के बाद छोटा वर्ग जोड़ें।
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भुजा (20-1) वाले वर्ग का क्षेत्र मॉडल किस संख्या का वर्ग दिखाता है?
The area model of a square with side (20-1) shows the square of which number?
#numeric model
#minus square
#visual identity
A (18)
B (19)
C (20)
D (21)
Explanation opens after your attempt
Step 1
Concept
(20-1=19). So this is the area model of \(19^2\).
Step 2
Why this answer is correct
The correct answer is B. (19). (20-1=19). So this is the area model of \(19^2\).
Step 3
Exam Tip
(20-1=19) है। इसलिए यह \(19^2\) का क्षेत्र मॉडल है।
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एक वर्ग की भुजा (a-b) है। उसका क्षेत्रफल किस रूप में लिखा जाएगा?
A square has side (a-b). How will its area be written?
#minus square
#area model
#algebraic identity
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
The area of the square is ((a-b)2 ). On expanding, it gives \(a^2-2ab+b^2\).
Step 2
Why this answer is correct
The correct answer is A. \(a^2-2ab+b^2\). The area of the square is ((a-b)2 ). On expanding, it gives \(a^2-2ab+b^2\).
Step 3
Exam Tip
वर्ग का क्षेत्रफल ((a-b)2 ) होता है। विस्तार करने पर \(a^2-2ab+b^2\) मिलता है।
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एक (5t-2) भुजा वाले वर्ग में घटाई गई दो पट्टियों का कुल क्षेत्रफल कितना है?
In a square of side (5t-2), what is the total area of the two subtracted strips?
#subtracted-strips
#minus-square
#area
A (10t)
B (20t)
C \(25t^2\)
D (4)
Explanation opens after your attempt
Step 1
Concept
The two strips are \(5t\cdot2\) and \(5t\cdot2\), so total (20t) is subtracted. In exams, include both strips.
Step 2
Why this answer is correct
The correct answer is B. (20t). The two strips are \(5t\cdot2\) and \(5t\cdot2\), so total (20t) is subtracted. In exams, include both strips.
Step 3
Exam Tip
दो पट्टियाँ \(5t\cdot2\) और \(5t\cdot2\) हैं, इसलिए कुल (20t) घटता है। परीक्षा में दोनों पट्टियाँ शामिल करें।
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यदि \(x^2-6x+9\) को दृश्य मॉडल से पढ़ना हो, तो कौन सा वर्ग बनता है?
If \(x^2-6x+9\) is read through a visual model, which square is formed?
#minus-square
#perfect-square
#visual-recognition
A भुजा (x+3) वाला वर्ग / Square with side (x+3)
B भुजा (x-3) वाला वर्ग / Square with side (x-3)
C भुजा (x-6) वाला वर्ग / Square with side (x-6)
D भुजा (x+9) वाला वर्ग / Square with side (x+9)
Explanation opens after your attempt
Correct Answer
B. भुजा (x-3) वाला वर्ग / Square with side (x-3)
Step 1
Concept
Since \(9=3^2\) and \(-6x=-2\times x\times3\), it is ((x-3)2 ). Exam tip: identify a subtraction square from the negative middle term.
Step 2
Why this answer is correct
The correct answer is B. भुजा (x-3) वाला वर्ग / Square with side (x-3). Since \(9=3^2\) and \(-6x=-2\times x\times3\), it is ((x-3)2 ). Exam tip: identify a subtraction square from the negative middle term.
Step 3
Exam Tip
\(9=3^2\) और \(-6x=-2\times x\times3\), इसलिए यह ((x-3)2 ) है। परीक्षा में ऋणात्मक बीच के पद से घटाव वर्ग पहचानें।
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किस मॉडल में \(4a^2-12ab+9b^2\) को एक पूर्ण वर्ग के रूप में देखा जा सकता है?
In which model can \(4a^2-12ab+9b^2\) be seen as a complete square?
#perfect-square-trinomial
#minus-square
#visual-recognition
A भुजा (2a-3b) वाला वर्ग / Square with side (2a-3b)
B भुजा (4a-9b) वाला वर्ग / Square with side (4a-9b)
C आयाम (2a+3b) और (2a-3b) वाला आयत / Rectangle with dimensions (2a+3b) and (2a-3b)
D भुजा (a-3b) वाला वर्ग / Square with side (a-3b)
Explanation opens after your attempt
Correct Answer
A. भुजा (2a-3b) वाला वर्ग / Square with side (2a-3b)
Step 1
Concept
Here (4a-2 =(2a)2 ), (9b-2 =(3b)2 ), and the middle term is \(-2\times2a\times3b\). Exam tip: match all three terms with the perfect square pattern.
Step 2
Why this answer is correct
The correct answer is A. भुजा (2a-3b) वाला वर्ग / Square with side (2a-3b). Here (4a-2 =(2a)2 ), (9b-2 =(3b)2 ), and the middle term is \(-2\times2a\times3b\). Exam tip: match all three terms with the perfect square pattern.
Step 3
Exam Tip
(4a-2 =(2a)2 ), (9b-2 =(3b)2 ) और बीच का पद \(-2\times2a\times3b\) है। परीक्षा में तीनों पदों को पूर्ण वर्ग पैटर्न से मिलाएं।
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यदि ((x-6)2 ) का दृश्य मॉडल \(x^2-12x+36\) देता है, तो (-12x) किससे आता है?
If the visual model of ((x-6)2 ) gives \(x^2-12x+36\), where does (-12x) come from?
#subtracted-strips
#minus-square
#visual-identity
A दो घटाए गए (6x) आयतों से / From two subtracted (6x) rectangles
B छोटे (36) वर्ग से / From the small (36) square
C बड़े \(x^2\) वर्ग से / From the large \(x^2\) square
D केवल भुजा (x-6) से / Only from the side (x-6)
Explanation opens after your attempt
Correct Answer
A. दो घटाए गए (6x) आयतों से / From two subtracted (6x) rectangles
Step 1
Concept
The total area of the two removed strips is (6x+6x=12x). Exam tip: connect the negative middle term with removed rectangles.
Step 2
Why this answer is correct
The correct answer is A. दो घटाए गए (6x) आयतों से / From two subtracted (6x) rectangles. The total area of the two removed strips is (6x+6x=12x). Exam tip: connect the negative middle term with removed rectangles.
Step 3
Exam Tip
दोनों हटाई गई पट्टियों का कुल क्षेत्र (6x+6x=12x) है। परीक्षा में ऋणात्मक बीच का पद हटाए गए आयतों से जोड़ें।
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भुजा (a-b) वाले वर्ग के मॉडल में \(a^2\) से दो (ab) पट्टियां हटाने के बाद \(b^2\) क्यों जोड़ा जाता है?
In the model of a square with side (a-b), why is \(b^2\) added after removing two (ab) strips from \(a^2\)?
#minus-square
#visual-proof
#over-subtraction
A क्योंकि \(b^2\) दो बार हट गया होता है / Because \(b^2\) has been removed twice
B क्योंकि \(b^2\) क्षेत्र शून्य होता है / Because \(b^2\) area is zero
C क्योंकि (ab) और \(b^2\) बराबर होते हैं / Because (ab) and \(b^2\) are equal
D क्योंकि \(a^2\) घटाना पड़ता है / Because \(a^2\) must be subtracted
Explanation opens after your attempt
Correct Answer
A. क्योंकि \(b^2\) दो बार हट गया होता है / Because \(b^2\) has been removed twice
Step 1
Concept
While removing two strips, the corner \(b^2\) part is subtracted twice. Exam tip: remember to add back the over-subtracted part.
Step 2
Why this answer is correct
The correct answer is A. क्योंकि \(b^2\) दो बार हट गया होता है / Because \(b^2\) has been removed twice. While removing two strips, the corner \(b^2\) part is subtracted twice. Exam tip: remember to add back the over-subtracted part.
Step 3
Exam Tip
दो पट्टियां हटाते समय कोने का \(b^2\) भाग दो बार घट जाता है। परीक्षा में अधिक घटे भाग को वापस जोड़ने का विचार याद रखें।
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यदि क्षेत्र मॉडल में \(x^2-12x+36\) का पूरा वर्ग बनता है, तो हटाए गए दो आयतों का कुल क्षेत्रफल कितना माना जाएगा?
If the area model forms the complete square \(x^2-12x+36\), what is considered the total area of the two removed rectangles?
#removed rectangles
#minus square
#visual model
A (6x)
B (12x)
C (36x)
D (72x)
Explanation opens after your attempt
Step 1
Concept
This is ((x-6)2 ), and the total area of the two removed rectangles is \(2\cdot6x=12x\). Exam tip: identify the subtracted middle area.
Step 2
Why this answer is correct
The correct answer is B. (12x). This is ((x-6)2 ), and the total area of the two removed rectangles is \(2\cdot6x=12x\). Exam tip: identify the subtracted middle area.
Step 3
Exam Tip
यह ((x-6)2 ) है और दो हटे आयतों का कुल क्षेत्रफल \(2\cdot6x=12x\) है। परीक्षा में घटाया गया मध्य क्षेत्र पहचानें।
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दृश्य मॉडल में \(x^2-8x+16\) को पूर्ण वर्ग दिखाने के लिए किस भुजा का वर्ग बनाया जाएगा?
To show \(x^2-8x+16\) as a perfect square in a visual model, a square of which side will be made?
#minus square
#complete square
#area model
A (x+4)
B (x-4)
C (x-8)
D (x+8)
Explanation opens after your attempt
Step 1
Concept
\(16=4^2\) and \(-8x=-2\cdot4x\), so the side is (x-4). Exam tip: read the negative middle term as a subtraction model.
Step 2
Why this answer is correct
The correct answer is B. (x-4). \(16=4^2\) and \(-8x=-2\cdot4x\), so the side is (x-4). Exam tip: read the negative middle term as a subtraction model.
Step 3
Exam Tip
\(16=4^2\) और \(-8x=-2\cdot4x\) है इसलिए भुजा (x-4) है। परीक्षा में ऋण मध्य पद को घटाव वाला मॉडल समझें।
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