एक वर्ग मॉडल में चार भाग \(4x^2\), (6xy), (6xy) और \(9y^2\) दिखते हैं। बाहरी भुजा कौन सी होगी?
A square model shows four parts \(4x^2\), (6xy), (6xy), and \(9y^2\). What will be the outer side?
#area model
#perfect square
#visual identity
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A (2x+3y)
B (4x+9y)
C (2x+6y)
D (4x+3y)
Explanation opens after your attempt
Correct Answer
A. (2x+3y)
Step 1
Concept
The parts \(4x^2\) and \(9y^2\) give side parts (2x) and (3y). Exam tip: identify the side parts from both square terms first.
Step 2
Why this answer is correct
The correct answer is A. (2x+3y). The parts \(4x^2\) and \(9y^2\) give side parts (2x) and (3y). Exam tip: identify the side parts from both square terms first.
Step 3
Exam Tip
भाग \(4x^2\) और \(9y^2\) से भुजाएँ (2x) और (3y) मिलती हैं। परीक्षा में दोनों वर्ग पदों की भुजाएँ पहले पहचानें।
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एक दृश्य मॉडल में \(a^2\) वर्ग से दो पट्टियाँ (ab) और (ab) हटती हैं पर कोना \(b^2\) दो बार हट जाता है। सही बचा क्षेत्रफल क्या होगा?
In a visual model, two strips (ab) and (ab) are removed from an \(a^2\) square but the corner \(b^2\) is removed twice. What is the correct remaining area?
#square of difference
#overlap model
#area subtraction
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A \(a^2-2ab-b^2\)
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
After subtracting two strips, \(b^2\) must be added back. Exam tip: watch the overlapping part carefully.
Step 2
Why this answer is correct
The correct answer is B. \(a^2-2ab+b^2\). After subtracting two strips, \(b^2\) must be added back. Exam tip: watch the overlapping part carefully.
Step 3
Exam Tip
दो पट्टियाँ घटाने के बाद \(b^2\) को वापस जोड़ना पड़ता है। परीक्षा में ओवरलैप वाले भाग को ध्यान से देखें।
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यदि \(x^2-b^2\) के कटे हुए मॉडल को आयत में बदला जाए और आयत की एक भुजा (x-b) हो, तो दूसरी भुजा क्या होगी?
If the cut model of \(x^2-b^2\) is rearranged into a rectangle and one side is (x-b), what is the other side?
#difference of squares
#rearrangement
#rectangle model
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A (x-b)
B (b-x)
C (x+b)
D \(x^2+b^2\)
Explanation opens after your attempt
Step 1
Concept
The difference of squares changes into ((x-b)(x+b)). Exam tip: the rectangle formed by cutting has difference and sum as sides.
Step 2
Why this answer is correct
The correct answer is C. (x+b). The difference of squares changes into ((x-b)(x+b)). Exam tip: the rectangle formed by cutting has difference and sum as sides.
Step 3
Exam Tip
वर्गों का अंतर ((x-b)(x+b)) में बदलता है। परीक्षा में कटकर बने आयत की भुजाएँ अंतर और योग होती हैं।
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एक आयत मॉडल की भुजाएँ (2m+5) और (2m-5) हैं। क्षेत्रफल का सही सरलीकृत रूप क्या है?
A rectangle model has sides (2m+5) and (2m-5). What is the correct simplified area?
#sum and difference
#visual rectangle
#hard identity
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A \(4m^2+25\)
B \(2m^2-25\)
C \(4m^2-10m+25\)
D \(4m^2-25\)
Explanation opens after your attempt
Correct Answer
D. \(4m^2-25\)
Step 1
Concept
This is product of sum and difference, so ((2m)2 -52 =4m-2 -25). Exam tip: square the whole (2m).
Step 2
Why this answer is correct
The correct answer is D. \(4m^2-25\). This is product of sum and difference, so ((2m)2 -52 =4m-2 -25). Exam tip: square the whole (2m).
Step 3
Exam Tip
यह योग और अंतर का गुणन है इसलिए ((2m)2 -52 =4m-2 -25) होगा। परीक्षा में पूरे (2m) का वर्ग करें।
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टाइल मॉडल में \(p^2+18p+81\) एक पूर्ण वर्ग बनाता है। यदि बीच का भाग दो बराबर आयतों से बना है, तो प्रत्येक आयत का क्षेत्रफल क्या होगा?
A tile model \(p^2+18p+81\) forms a perfect square. If the middle part is made of two equal rectangles, what is the area of each rectangle?
#algebra tiles
#middle rectangles
#perfect square
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A (9p)
B (18p)
C (81p)
D (p+9)
Explanation opens after your attempt
Step 1
Concept
The total middle term is (18p), so each equal rectangle is (9p). Exam tip: split (2ab) into two equal rectangles.
Step 2
Why this answer is correct
The correct answer is A. (9p). The total middle term is (18p), so each equal rectangle is (9p). Exam tip: split (2ab) into two equal rectangles.
Step 3
Exam Tip
बीच का कुल पद (18p) है इसलिए प्रत्येक बराबर आयत (9p) होगा। परीक्षा में (2ab) को दो समान आयतों में बाँटें।
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एक वर्ग की बाहरी भुजा (3a-2b) है। दृश्य मॉडल के आधार पर बीच का पद क्या होगा?
The outer side of a square is (3a-2b). Based on the visual model, what will be the middle term?
#square of difference
#sign
#area model
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A (12ab)
B (6ab)
C (-12ab)
D (-6ab)
Explanation opens after your attempt
Correct Answer
C. (-12ab)
Step 1
Concept
The middle term is \(2\cdot 3a\cdot -2b=-12ab\). Exam tip: do not forget the sign of the subtraction part.
Step 2
Why this answer is correct
The correct answer is C. (-12ab). The middle term is \(2\cdot 3a\cdot -2b=-12ab\). Exam tip: do not forget the sign of the subtraction part.
Step 3
Exam Tip
बीच का पद \(2\cdot 3a\cdot -2b=-12ab\) है। परीक्षा में घटाव वाले भाग का चिन्ह न भूलें।
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चित्र में ((x+4)(x+7)) का आयत चार भागों में है। कौन सा भाग कोने के छोटे आयत का क्षेत्रफल होगा?
A rectangle for ((x+4)(x+7)) is divided into four parts. Which part is the area of the small corner rectangle?
#rectangle model
#constant product
#visual multiplication
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A (11x)
B (28)
C (4x)
D (7x)
Explanation opens after your attempt
Step 1
Concept
The small corner area is \(4\cdot 7=28\). Exam tip: identify the product of constant parts separately.
Step 2
Why this answer is correct
The correct answer is B. (28). The small corner area is \(4\cdot 7=28\). Exam tip: identify the product of constant parts separately.
Step 3
Exam Tip
छोटे कोने का क्षेत्रफल \(4\cdot 7=28\) है। परीक्षा में स्थिर भागों के गुणन को अलग पहचानें।
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यदि \(x^2+kx+36\) का टाइल मॉडल भुजा (x+6) वाला पूर्ण वर्ग है, तो (k) का मान क्या होगा?
If the tile model \(x^2+kx+36\) is a perfect square with side (x+6), what is the value of (k)?
#missing coefficient
#tile model
#perfect square
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A (6)
B (18)
C (12)
D (36)
Explanation opens after your attempt
Step 1
Concept
((x+6)2 =x-2 +12x+36), so (k=12). Exam tip: get the middle term from (2ab).
Step 2
Why this answer is correct
The correct answer is C. (12). ((x+6)2 =x-2 +12x+36), so (k=12). Exam tip: get the middle term from (2ab).
Step 3
Exam Tip
((x+6)2 =x-2 +12x+36) है इसलिए (k=12) होगा। परीक्षा में बीच का पद (2ab) से निकालें।
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एक मॉडल में \(a^2-b^2\) को काटकर आयत बनाया गया। यदि आयत की लंबाई (15) और चौड़ाई (7) है, तो (a) और (b) के लिए सही जोड़ा कौन सा हो सकता है?
In a model, \(a^2-b^2\) is cut and rearranged into a rectangle. If the rectangle length is (15) and breadth is (7), which pair for (a) and (b) can be correct?
#difference of squares
#reverse model
#area
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A (a=11,\ b=4)
B (a=15,\ b=7)
C (a=8,\ b=7)
D (a=22,\ b=8)
Explanation opens after your attempt
Correct Answer
A. (a=11,\ b=4)
Step 1
Concept
The rectangle sides are (a+b=15) and (a-b=7), so (a=11) and (b=4). Exam tip: find the two numbers from sum and difference.
Step 2
Why this answer is correct
The correct answer is A. (a=11,\ b=4). The rectangle sides are (a+b=15) and (a-b=7), so (a=11) and (b=4). Exam tip: find the two numbers from sum and difference.
Step 3
Exam Tip
आयत की भुजाएँ (a+b=15) और (a-b=7) हैं इसलिए (a=11) और (b=4)। परीक्षा में योग और अंतर से दो संख्याएँ निकालें।
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भुजा (2x+3) वाले वर्ग में (x) वाले दोनों आयतों का संयुक्त क्षेत्रफल कितना होगा?
In a square of side (2x+3), what is the combined area of the two (x)-rectangles?
#middle area
#binomial square
#visual model
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A (6x)
B (9x)
C (12x)
D \(4x^2\)
Explanation opens after your attempt
Step 1
Concept
The sum of the two rectangles is \(2\cdot 2x\cdot 3=12x\). Exam tip: treat (2x) as one complete part.
Step 2
Why this answer is correct
The correct answer is C. (12x). The sum of the two rectangles is \(2\cdot 2x\cdot 3=12x\). Exam tip: treat (2x) as one complete part.
Step 3
Exam Tip
दोनों आयतों का योग \(2\cdot 2x\cdot 3=12x\) है। परीक्षा में (2x) को एक पूरा भाग मानें।
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एक दृश्य प्रमाण में \(a^2+2ab+b^2\) और \(a^2-b^2\) दोनों दिखाई देते हैं। कौन सा कथन सही है?
In a visual proof, both \(a^2+2ab+b^2\) and \(a^2-b^2\) appear. Which statement is correct?
#identity comparison
#visual proof
#area
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A पहला योग के वर्ग से और दूसरा वर्गों के अंतर से जुड़ा है / The first is linked to square of sum and the second to difference of squares
B दोनों हमेशा समान क्षेत्रफल होते हैं / Both always have equal area
C दोनों केवल परिमाप बताते हैं / Both show only perimeter
D पहला घटाव और दूसरा जोड़ दिखाता है / The first shows subtraction and the second shows addition
Explanation opens after your attempt
Correct Answer
A. पहला योग के वर्ग से और दूसरा वर्गों के अंतर से जुड़ा है / The first is linked to square of sum and the second to difference of squares
Step 1
Concept
(a-2 +2ab+b-2 =(a+b)2 ) and (a-2 -b-2 =(a+b)(a-b)). Exam tip: identify the type of model.
Step 2
Why this answer is correct
The correct answer is A. पहला योग के वर्ग से और दूसरा वर्गों के अंतर से जुड़ा है / The first is linked to square of sum and the second to difference of squares. (a-2 +2ab+b-2 =(a+b)2 ) and (a-2 -b-2 =(a+b)(a-b)). Exam tip: identify the type of model.
Step 3
Exam Tip
(a-2 +2ab+b-2 =(a+b)2 ) और (a-2 -b-2 =(a+b)(a-b)) हैं। परीक्षा में मॉडल का प्रकार पहचानें।
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यदि वर्ग मॉडल में \(9x^2\) और (16) कोने के वर्ग हैं तथा बीच का पद ऋणात्मक है, तो सही क्षेत्रफल कौन सा होगा?
If a square model has corner squares \(9x^2\) and (16) and the middle term is negative, what is the correct area?
#negative middle term
#square model
#identity
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A \(9x^2+24x+16\)
B \(9x^2-24x+16\)
C \(3x^2-8x+16\)
D \(9x^2-16\)
Explanation opens after your attempt
Correct Answer
B. \(9x^2-24x+16\)
Step 1
Concept
The side parts are (3x) and (4), so the subtraction square is ((3x-4)2 ). Exam tip: identify the negative middle sign.
Step 2
Why this answer is correct
The correct answer is B. \(9x^2-24x+16\). The side parts are (3x) and (4), so the subtraction square is ((3x-4)2 ). Exam tip: identify the negative middle sign.
Step 3
Exam Tip
भुजाएँ (3x) और (4) हैं इसलिए घटाव वाला वर्ग ((3x-4)2 ) है। परीक्षा में बीच का ऋण चिन्ह पहचानें।
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एक आयत मॉडल में क्षेत्रफल \(x^2+9x+20\) है और छोटे कोने का क्षेत्रफल (20) है। कौन सी भुजाएँ संभव हैं?
A rectangle model has area \(x^2+9x+20\) and the small corner area is (20). Which sides are possible?
#factor rectangle
#area model
#quadratic identity
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A (x+2) और (x+10) / (x+2) and (x+10)
B (x+4) और (x+5) / (x+4) and (x+5)
C (x+1) और (x+20) / (x+1) and (x+20)
D (x+3) और (x+6) / (x+3) and (x+6)
Explanation opens after your attempt
Correct Answer
B. (x+4) और (x+5) / (x+4) and (x+5)
Step 1
Concept
The numbers (4) and (5) have product (20) and sum (9). Exam tip: check corner product and middle sum together.
Step 2
Why this answer is correct
The correct answer is B. (x+4) और (x+5) / (x+4) and (x+5). The numbers (4) and (5) have product (20) and sum (9). Exam tip: check corner product and middle sum together.
Step 3
Exam Tip
संख्याएँ (4) और (5) का गुणन (20) और योग (9) है। परीक्षा में कोने का गुणन और बीच का योग साथ देखें।
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भुजा (5p-q) वाले वर्ग में (pq) वाला संयुक्त मध्य क्षेत्रफल कौन सा होगा?
In a square of side (5p-q), what is the combined middle area containing (pq)?
#square difference
#combined middle area
#sign
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A (5pq)
B (10pq)
C (-10pq)
D (25pq)
Explanation opens after your attempt
Correct Answer
C. (-10pq)
Step 1
Concept
The combined middle area is \(2\cdot 5p\cdot -q=-10pq\). Exam tip: write subtraction in the visual model as a negative term.
Step 2
Why this answer is correct
The correct answer is C. (-10pq). The combined middle area is \(2\cdot 5p\cdot -q=-10pq\). Exam tip: write subtraction in the visual model as a negative term.
Step 3
Exam Tip
बीच का संयुक्त क्षेत्रफल \(2\cdot 5p\cdot -q=-10pq\) है। परीक्षा में दृश्य मॉडल में घटाव को ऋणात्मक क्षेत्रफल के रूप में लिखें।
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यदि ((a+b)2 ) मॉडल में \(a^2+b^2\) भागों का योग (85) है और दो आयतों का योग (84) है, तो पूरे वर्ग का क्षेत्रफल क्या होगा?
If in a ((a+b)2 ) model, the sum of \(a^2+b^2\) parts is (85) and the sum of two rectangles is (84), what is the area of the whole square?
#area sum
#visual square
#numerical identity
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A (169)
B (1)
C (85)
D (84)
Explanation opens after your attempt
Step 1
Concept
The total area is \(a^2+2ab+b^2=85+84=169\). Exam tip: the sum of all parts gives total area.
Step 2
Why this answer is correct
The correct answer is A. (169). The total area is \(a^2+2ab+b^2=85+84=169\). Exam tip: the sum of all parts gives total area.
Step 3
Exam Tip
पूरा क्षेत्रफल \(a^2+2ab+b^2=85+84=169\) है। परीक्षा में सभी भागों का योग कुल क्षेत्रफल देता है।
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किस मॉडल में \(x^2-49\) को बिना विस्तार किए सीधे आयत की भुजाओं के रूप में पढ़ा जा सकता है?
In which model can \(x^2-49\) be read directly as rectangle sides without expansion?
#difference of squares
#rectangle sides
#visual factor
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A भुजाएँ (x+7) और (x-7) वाला आयत / Rectangle with sides (x+7) and (x-7)
B भुजा (x+7) वाला वर्ग / Square with side (x+7)
C भुजा (x-7) वाला वर्ग / Square with side (x-7)
D भुजाएँ (x) और (49) वाला आयत / Rectangle with sides (x) and (49)
Explanation opens after your attempt
Correct Answer
A. भुजाएँ (x+7) और (x-7) वाला आयत / Rectangle with sides (x+7) and (x-7)
Step 1
Concept
(x-2 -49=x-2 -72 =(x+7)(x-7)). Exam tip: see (49) as \(7^2\).
Step 2
Why this answer is correct
The correct answer is A. भुजाएँ (x+7) और (x-7) वाला आयत / Rectangle with sides (x+7) and (x-7). (x-2 -49=x-2 -72 =(x+7)(x-7)). Exam tip: see (49) as \(7^2\).
Step 3
Exam Tip
(x-2 -49=x-2 -72 =(x+7)(x-7)) है। परीक्षा में (49) को \(7^2\) की तरह देखें।
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एक वर्ग मॉडल का क्षेत्रफल \(16a^2+40ab+25b^2\) है। बाहरी भुजा कौन सी होगी?
The area of a square model is \(16a^2+40ab+25b^2\). What will be the outer side?
#perfect square trinomial
#visual model
#side
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A (16a+25b)
B (4a+5b)
C (8a+5b)
D (4a+10b)
Explanation opens after your attempt
Correct Answer
B. (4a+5b)
Step 1
Concept
(16a-2 =(4a)2 ) and (25b-2 =(5b)2 ), and the middle term is (40ab). Exam tip: add the roots of both squares.
Step 2
Why this answer is correct
The correct answer is B. (4a+5b). (16a-2 =(4a)2 ) and (25b-2 =(5b)2 ), and the middle term is (40ab). Exam tip: add the roots of both squares.
Step 3
Exam Tip
(16a-2 =(4a)2 ) और (25b-2 =(5b)2 ), बीच का पद भी (40ab) है। परीक्षा में दोनों वर्गों के मूल जोड़ें।
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एक आयत मॉडल में ((3x+2)(x+5)) है। चार भागों में (x) वाले पदों का संयुक्त योग क्या होगा?
A rectangle model represents ((3x+2)(x+5)). What is the combined sum of the (x)-terms in the four parts?
#rectangle multiplication
#like terms
#area model
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A (15x)
B (2x)
C (17x)
D (10x)
Explanation opens after your attempt
Step 1
Concept
The four parts include like terms (15x) and (2x), whose sum is (17x). Exam tip: combine like terms.
Step 2
Why this answer is correct
The correct answer is C. (17x). The four parts include like terms (15x) and (2x), whose sum is (17x). Exam tip: combine like terms.
Step 3
Exam Tip
चार भागों में (15x) और (2x) जैसे पद मिलते हैं जिनका योग (17x) है। परीक्षा में जैसे पदों को जोड़ें।
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यदि ((2x-3)2 ) का दृश्य मॉडल बनाया जाए, तो कौन सा क्षेत्रफल घटाने और जोड़ने के बाद सही अंतिम रूप देता है?
If a visual model of ((2x-3)2 ) is made, which area expression gives the correct final form after subtraction and addition?
#square of difference
#visual expansion
#coefficient
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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
In ((2x-3)2 ), the middle term \(2\cdot 2x\cdot 3=12x\) is negative. Exam tip: square the coefficient of the first term.
Step 2
Why this answer is correct
The correct answer is A. \(4x^2-12x+9\). In ((2x-3)2 ), the middle term \(2\cdot 2x\cdot 3=12x\) is negative. Exam tip: square the coefficient of the first term.
Step 3
Exam Tip
((2x-3)2 ) में बीच का पद \(2\cdot 2x\cdot 3=12x\) ऋणात्मक होता है। परीक्षा में पहले पद के गुणांक का वर्ग करें।
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एक कट और चिपकाओ मॉडल में \(a^2-b^2\) का क्षेत्रफल (96) है और (a-b=6) है। (a+b) क्या होगा?
In a cut-and-paste model, the area of \(a^2-b^2\) is (96) and (a-b=6). What is (a+b)?
#cut paste model
#difference of squares
#unknown side
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A (90)
B (16)
C (102)
D (12)
Explanation opens after your attempt
Step 1
Concept
(a-2 -b-2 =(a-b)(a+b)), so (96=6(a+b)). Exam tip: divide to find the other side of the rectangle.
Step 2
Why this answer is correct
The correct answer is B. (16). (a-2 -b-2 =(a-b)(a+b)), so (96=6(a+b)). Exam tip: divide to find the other side of the rectangle.
Step 3
Exam Tip
(a-2 -b-2 =(a-b)(a+b)) है इसलिए (96=6(a+b))। परीक्षा में आयत की दूसरी भुजा भाग देकर निकालें।
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एक वर्ग मॉडल में बाहरी क्षेत्रफल ((x+y)2 ) है और दो छोटे वर्गों का योग \(x^2+y^2\) है। दो आयतों का संयुक्त क्षेत्रफल क्या होगा?
In a square model, the outer area is ((x+y)2 ) and the sum of two small squares is \(x^2+y^2\). What is the combined area of the two rectangles?
#rectangle parts
#area difference
#visual square
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A (xy)
B (x+y)
C (2xy)
D \(x^2-y^2\)
Explanation opens after your attempt
Step 1
Concept
The total area of the two rectangles is ((x+y)2 -\(x^2+y^2\)=2xy). Exam tip: subtract the sum of squares from the whole area.
Step 2
Why this answer is correct
The correct answer is C. (2xy). The total area of the two rectangles is ((x+y)2 -\(x^2+y^2\)=2xy). Exam tip: subtract the sum of squares from the whole area.
Step 3
Exam Tip
दो आयतों का कुल क्षेत्रफल ((x+y)2 -\(x^2+y^2\)=2xy) है। परीक्षा में पूरे क्षेत्रफल से वर्गों का योग घटाएँ।
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यदि \(x^2+10x+c\) का टाइल मॉडल भुजा (x+5) वाला वर्ग बनता है, तो (c) कौन सा होगा?
If the tile model \(x^2+10x+c\) forms a square with side (x+5), what is (c)?
#missing constant
#tile model
#complete square
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A (10)
B (15)
C (20)
D (25)
Explanation opens after your attempt
Step 1
Concept
The constant part of the side is (5), so the small corner square is \(5^2=25\). Exam tip: the last term is the square of the constant part.
Step 2
Why this answer is correct
The correct answer is D. (25). The constant part of the side is (5), so the small corner square is \(5^2=25\). Exam tip: the last term is the square of the constant part.
Step 3
Exam Tip
भुजा का स्थिर भाग (5) है इसलिए कोने का छोटा वर्ग \(5^2=25\) होगा। परीक्षा में अंतिम पद स्थिर भाग का वर्ग होता है।
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किस दृश्य विभाजन से ((a+b+c)2 ) का (2ab+2bc+2ca) वाला भाग समझ में आता है?
Which visual partition explains the (2ab+2bc+2ca) part of ((a+b+c)2 )?
#three term square
#visual partition
#pair rectangles
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A तीन वर्गों से ही / From only three squares
B सभी जोड़ीदार आयतों की दो दो प्रतियों से / From two copies of each pairwise rectangle
C सिर्फ एक (abc) घन से / From only one (abc) cube
D केवल बाहरी परिमाप से / From only the outer perimeter
Explanation opens after your attempt
Correct Answer
B. सभी जोड़ीदार आयतों की दो दो प्रतियों से / From two copies of each pairwise rectangle
Step 1
Concept
In a three-part square, (ab), (bc), and (ca) rectangles appear twice each. Exam tip: count pairwise rectangles.
Step 2
Why this answer is correct
The correct answer is B. सभी जोड़ीदार आयतों की दो दो प्रतियों से / From two copies of each pairwise rectangle. In a three-part square, (ab), (bc), and (ca) rectangles appear twice each. Exam tip: count pairwise rectangles.
Step 3
Exam Tip
तीन भागों वाले वर्ग में (ab), (bc) और (ca) आयत दो दो बार आते हैं। परीक्षा में जोड़ीदार आयतों को गिनें।
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एक आयत मॉडल में ((2x+1)(2x+7)) है। कुल क्षेत्रफल में स्थिर कोना और (x) वाले संयुक्त पद कौन से होंगे?
A rectangle model represents ((2x+1)(2x+7)). What will be the constant corner and combined (x)-term in the total area?
#rectangle area
#combined terms
#visual multiplication
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A (7) और (16x) / (7) and (16x)
B (14) और (8x) / (14) and (8x)
C (7) और (8x) / (7) and (8x)
D (1) और (14x) / (1) and (14x)
Explanation opens after your attempt
Correct Answer
A. (7) और (16x) / (7) and (16x)
Step 1
Concept
The constant corner is \(1\cdot 7=7\) and the (x)-terms are (14x+2x=16x). Exam tip: add the four parts separately.
Step 2
Why this answer is correct
The correct answer is A. (7) और (16x) / (7) and (16x). The constant corner is \(1\cdot 7=7\) and the (x)-terms are (14x+2x=16x). Exam tip: add the four parts separately.
Step 3
Exam Tip
स्थिर कोना \(1\cdot 7=7\) और (x) पद (14x+2x=16x) हैं। परीक्षा में चार भागों को अलग जोड़ें।
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यदि किसी वर्ग मॉडल का क्षेत्रफल \(25x^2-30xy+9y^2\) है, तो उसकी भुजा क्या होगी?
If the area of a square model is \(25x^2-30xy+9y^2\), what is its side?
#perfect square
#negative middle
#visual model
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A (5x+3y)
B (25x-9y)
C (5x-3y)
D (10x-6y)
Explanation opens after your attempt
Correct Answer
C. (5x-3y)
Step 1
Concept
This is the expansion of ((5x-3y)2 ) because the middle term is (-30xy). Exam tip: identify subtraction in the side from the negative middle term.
Step 2
Why this answer is correct
The correct answer is C. (5x-3y). This is the expansion of ((5x-3y)2 ) because the middle term is (-30xy). Exam tip: identify subtraction in the side from the negative middle term.
Step 3
Exam Tip
यह ((5x-3y)2 ) का विस्तार है क्योंकि बीच का पद (-30xy) है। परीक्षा में ऋणात्मक मध्य पद से भुजा में घटाव पहचानें।
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दृश्य मॉडल में \(a^2+2ab+b^2\) का कुल क्षेत्रफल (144) है। यदि (a+b) धनात्मक है, तो बाहरी भुजा क्या होगी?
In a visual model, the total area \(a^2+2ab+b^2\) is (144). If (a+b) is positive, what is the outer side?
#outer side
#total area
#square model
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A (24)
B (72)
C (12)
D (144)
Explanation opens after your attempt
Step 1
Concept
The total area is ((a+b)2 =144), so the outer side is (12). Exam tip: take square root of area to get the side.
Step 2
Why this answer is correct
The correct answer is C. (12). The total area is ((a+b)2 =144), so the outer side is (12). Exam tip: take square root of area to get the side.
Step 3
Exam Tip
कुल क्षेत्रफल ((a+b)2 =144) है इसलिए बाहरी भुजा (12) होगी। परीक्षा में क्षेत्रफल का वर्गमूल लेकर भुजा निकालें।
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यदि (a+b=13) और (a-b=5) हैं, तो \(a^2-b^2\) के आयत मॉडल का क्षेत्रफल कितना होगा?
If (a+b=13) and (a-b=5), what is the area of the rectangle model of \(a^2-b^2\)?
#difference of squares
#area shortcut
#visual rectangle
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A (18)
B (65)
C (169)
D (25)
Explanation opens after your attempt
Step 1
Concept
The difference of squares is ((a+b)(a-b)=13\cdot 5=65). Exam tip: no need to find (a) and (b) separately.
Step 2
Why this answer is correct
The correct answer is B. (65). The difference of squares is ((a+b)(a-b)=13\cdot 5=65). Exam tip: no need to find (a) and (b) separately.
Step 3
Exam Tip
वर्गों का अंतर ((a+b)(a-b)=13\cdot 5=65) है। परीक्षा में (a) और (b) अलग निकालने की जरूरत नहीं होती।
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एक वर्ग मॉडल में बाहरी भुजा (x+y) है। यदि (x) भाग को दोगुना करके भुजा (2x+y) कर दी जाए, तो \(y^2\) को छोड़कर नया कौन सा अतिरिक्त (x) आधारित भाग बनेगा?
A square model has outer side (x+y). If the (x)-part is doubled to make side (2x+y), what new (x)-based part appears apart from \(y^2\)?
#changed side
#visual square
#binomial identity
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A \(4x^2+4xy\)
B \(x^2+2xy\)
C \(2x^2+xy\)
D \(4x^2+2xy\)
Explanation opens after your attempt
Correct Answer
A. \(4x^2+4xy\)
Step 1
Concept
((2x+y)2 =4x-2 +4xy+y-2 ). Exam tip: apply the square formula to the changed side.
Step 2
Why this answer is correct
The correct answer is A. \(4x^2+4xy\). ((2x+y)2 =4x-2 +4xy+y-2 ). Exam tip: apply the square formula to the changed side.
Step 3
Exam Tip
((2x+y)2 =4x-2 +4xy+y-2 ) है। परीक्षा में बदली हुई भुजा पर पूरा वर्ग सूत्र लगाएँ।
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टाइल मॉडल में ((x-4)2 ) बनाने के लिए \(x^2\) वर्ग से किन क्षेत्रों को घटाकर किस क्षेत्र को वापस जोड़ा जाता है?
In a tile model for ((x-4)2 ), which areas are subtracted from the \(x^2\) square and which area is added back?
#tile removal
#overlap
#square of difference
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A (4x) और (4x) घटाकर (16) जोड़ा जाता है / Subtract (4x) and (4x), then add (16)
B (16x) घटाकर (4) जोड़ा जाता है / Subtract (16x), then add (4)
C (8x) जोड़कर (16) घटाया जाता है / Add (8x), then subtract (16)
D \(x^2\) घटाकर (16x) जोड़ा जाता है / Subtract \(x^2\), then add (16x)
Explanation opens after your attempt
Correct Answer
A. (4x) और (4x) घटाकर (16) जोड़ा जाता है / Subtract (4x) and (4x), then add (16)
Step 1
Concept
Two (4x) strips are subtracted and the corner (16) is added back. Exam tip: avoid subtracting the overlap twice.
Step 2
Why this answer is correct
The correct answer is A. (4x) और (4x) घटाकर (16) जोड़ा जाता है / Subtract (4x) and (4x), then add (16). Two (4x) strips are subtracted and the corner (16) is added back. Exam tip: avoid subtracting the overlap twice.
Step 3
Exam Tip
दो (4x) पट्टियाँ घटती हैं और कोने का (16) भाग वापस जुड़ता है। परीक्षा में ओवरलैप को दो बार घटने से बचाएँ।
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एक आयत मॉडल \(x^2+bx+24\) को ((x+3)(x+c)) के रूप में दिखाता है। (b) और (c) क्या होंगे?
A rectangle model shows \(x^2+bx+24\) as ((x+3)(x+c)). What are (b) and (c)?
#unknown side
#rectangle factor
#area model
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A (b=8,\ c=5)
B (b=11,\ c=8)
C (b=27,\ c=24)
D (b=6,\ c=3)
Explanation opens after your attempt
Correct Answer
B. (b=11,\ c=8)
Step 1
Concept
The corner area (3c=24) gives (c=8), and (b=3+8=11). Exam tip: solve the corner first.
Step 2
Why this answer is correct
The correct answer is B. (b=11,\ c=8). The corner area (3c=24) gives (c=8), and (b=3+8=11). Exam tip: solve the corner first.
Step 3
Exam Tip
कोने का क्षेत्रफल (3c=24) देता है इसलिए (c=8) और (b=3+8=11)। परीक्षा में कोना पहले हल करें।
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यदि वर्ग मॉडल में \(a^2+2ab+b^2\) है पर किसी विद्यार्थी ने केवल \(a^2+b^2\) लिखा, तो कौन सा दृश्य भाग छूट गया?
If a square model has \(a^2+2ab+b^2\) but a student wrote only \(a^2+b^2\), which visual part was missed?
#common error
#visual identity
#missing rectangles
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A दो (ab) आयत / Two (ab) rectangles
B एक \(a^2\) वर्ग / One \(a^2\) square
C एक \(b^2\) वर्ग / One \(b^2\) square
D बाहरी भुजा (a+b) / Outer side (a+b)
Explanation opens after your attempt
Correct Answer
A. दो (ab) आयत / Two (ab) rectangles
Step 1
Concept
The missed part is (2ab), made of two (ab) rectangles. Exam tip: never omit the middle rectangles.
Step 2
Why this answer is correct
The correct answer is A. दो (ab) आयत / Two (ab) rectangles. The missed part is (2ab), made of two (ab) rectangles. Exam tip: never omit the middle rectangles.
Step 3
Exam Tip
छूटा हुआ भाग (2ab) है जो दो (ab) आयतों से बनता है। परीक्षा में बीच के आयतों को कभी न छोड़ें।
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एक क्षेत्रफल मॉडल में ((4x+3y)(4x-3y)) दिखाया गया है। कौन सा क्षेत्रफल सही है?
An area model shows ((4x+3y)(4x-3y)). Which area is correct?
#sum difference
#cancellation
#visual model
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A \(16x^2+9y^2\)
B \(8x^2-6y^2\)
C \(16x^2-9y^2\)
D \(16x^2-24xy+9y^2\)
Explanation opens after your attempt
Correct Answer
C. \(16x^2-9y^2\)
Step 1
Concept
In product of sum and difference, the middle terms cancel. Exam tip: remember ((A+B)(A-B)=A-2 -B-2 ).
Step 2
Why this answer is correct
The correct answer is C. \(16x^2-9y^2\). In product of sum and difference, the middle terms cancel. Exam tip: remember ((A+B)(A-B)=A-2 -B-2 ).
Step 3
Exam Tip
योग और अंतर के गुणन में बीच के पद कट जाते हैं। परीक्षा में ((A+B)(A-B)=A-2 -B-2 ) याद रखें।
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यदि ((x+a)2 ) के वर्ग मॉडल में प्रत्येक आयत का क्षेत्रफल (11x) है, तो अंतिम छोटा वर्ग क्या होगा?
If in the square model of ((x+a)2 ), each rectangle has area (11x), what will the final small square be?
#unknown constant
#algebra tiles
#perfect square
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A (22)
B (121)
C \(11x^2\)
D (22x)
Explanation opens after your attempt
Step 1
Concept
Each rectangle is (ax=11x), so (a=11) and the small square is (121). Exam tip: identify the constant side from one rectangle.
Step 2
Why this answer is correct
The correct answer is B. (121). Each rectangle is (ax=11x), so (a=11) and the small square is (121). Exam tip: identify the constant side from one rectangle.
Step 3
Exam Tip
प्रत्येक आयत (ax=11x) है इसलिए (a=11) और छोटा वर्ग (121) है। परीक्षा में एक आयत से स्थिर भुजा पहचानें।
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भुजा (x+2y+3z) वाले वर्ग के मॉडल में (yz) वाले आयतों का संयुक्त क्षेत्रफल क्या होगा?
In the square model of side (x+2y+3z), what is the combined area of the rectangles containing (yz)?
#three part square
#yz rectangles
#visual expansion
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A (5yz)
B (12yz)
C (6yz)
D (3yz)
Explanation opens after your attempt
Step 1
Concept
Two rectangles from (2y) and (3z) appear, so \(2\cdot 2y\cdot 3z=12yz\). Exam tip: count pairwise rectangles in a three-part square.
Step 2
Why this answer is correct
The correct answer is B. (12yz). Two rectangles from (2y) and (3z) appear, so \(2\cdot 2y\cdot 3z=12yz\). Exam tip: count pairwise rectangles in a three-part square.
Step 3
Exam Tip
(2y) और (3z) के दो आयत मिलते हैं इसलिए \(2\cdot 2y\cdot 3z=12yz\)। परीक्षा में तीन भागों वाले वर्ग में जोड़ीदार आयत गिनें।
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एक वर्ग मॉडल का क्षेत्रफल \(x^2+14x+49\) है। यदि बाहरी भुजा (x+k) है, तो (k) क्या होगा?
The area of a square model is \(x^2+14x+49\). If the outer side is (x+k), what is (k)?
#parameter side
#perfect square
#visual model
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A (14)
B (21)
C (7)
D (49)
Explanation opens after your attempt
Step 1
Concept
\(49=7^2\) and \(2\cdot x\cdot 7=14x\), so (k=7). Exam tip: check both square root of last term and middle term.
Step 2
Why this answer is correct
The correct answer is C. (7). \(49=7^2\) and \(2\cdot x\cdot 7=14x\), so (k=7). Exam tip: check both square root of last term and middle term.
Step 3
Exam Tip
\(49=7^2\) और \(2\cdot x\cdot 7=14x\), इसलिए (k=7)। परीक्षा में अंतिम पद का वर्गमूल और मध्य पद दोनों जाँचें।
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यदि \(a^2-b^2=45\) का आयत मॉडल बना है और (a+b=9), तो आयत की दूसरी भुजा (a-b) क्या होगी?
If a rectangle model of \(a^2-b^2=45\) is made and (a+b=9), what is the other side (a-b)?
#difference of squares
#unknown breadth
#rectangle model
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A (36)
B (5)
C (54)
D (405)
Explanation opens after your attempt
Step 1
Concept
(45=(a+b)(a-b)=9(a-b)), so (a-b=5). Exam tip: divide the area by the known side.
Step 2
Why this answer is correct
The correct answer is B. (5). (45=(a+b)(a-b)=9(a-b)), so (a-b=5). Exam tip: divide the area by the known side.
Step 3
Exam Tip
(45=(a+b)(a-b)=9(a-b)), इसलिए (a-b=5)। परीक्षा में क्षेत्रफल को ज्ञात भुजा से भाग दें।
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किस दृश्य मॉडल से यह गलती पकड़ी जा सकती है कि ((x+5)2 =x-2 +25) नहीं है?
Which visual model can catch the mistake that ((x+5)2 ) is not \(x^2+25\)?
#error analysis
#missing middle term
#visual square
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A दो (5x) आयतों वाला वर्ग मॉडल / Square model with two (5x) rectangles
B केवल एक \(x^2\) टाइल / Only one \(x^2\) tile
C भुजा (x-5) वाला आयत / Rectangle with side (x-5)
D भुजाएँ (x+5) और (x-5) वाला आयत / Rectangle with sides (x+5) and (x-5)
Explanation opens after your attempt
Correct Answer
A. दो (5x) आयतों वाला वर्ग मॉडल / Square model with two (5x) rectangles
Step 1
Concept
The correct model has two (5x) rectangles along with \(x^2\) and (25). Exam tip: omitting the middle term is a common mistake.
Step 2
Why this answer is correct
The correct answer is A. दो (5x) आयतों वाला वर्ग मॉडल / Square model with two (5x) rectangles. The correct model has two (5x) rectangles along with \(x^2\) and (25). Exam tip: omitting the middle term is a common mistake.
Step 3
Exam Tip
सही मॉडल में \(x^2\) और (25) के साथ दो (5x) आयत भी होते हैं। परीक्षा में बीच का पद छोड़ना सबसे सामान्य गलती है।
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एक आयत के भाग \(6x^2\), (9x), (4x) और (6) हैं। कौन सा गुणनफल इस मॉडल को सही दिखाता है?
The parts of a rectangle are \(6x^2\), (9x), (4x), and (6). Which product correctly represents this model?
#area decomposition
#rectangle factors
#visual multiplication
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A ((3x+2)(2x+3))
B ((6x+1)(x+6))
C ((2x+2)(3x+3))
D ((3x+6)(2x+1))
Explanation opens after your attempt
Correct Answer
A. ((3x+2)(2x+3))
Step 1
Concept
((3x+2)(2x+3)) gives \(6x^2\), (9x), (4x), and (6). Exam tip: verify all four areas.
Step 2
Why this answer is correct
The correct answer is A. ((3x+2)(2x+3)). ((3x+2)(2x+3)) gives \(6x^2\), (9x), (4x), and (6). Exam tip: verify all four areas.
Step 3
Exam Tip
((3x+2)(2x+3)) से \(6x^2\), (9x), (4x) और (6) मिलते हैं। परीक्षा में चारों क्षेत्रफल मिलाकर जाँचें।
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यदि भुजा (a+b) वाले वर्ग और भुजा (a-b) वाले वर्ग के क्षेत्रफलों का अंतर लिया जाए, तो दृश्य रूप से कौन सा क्षेत्रफल मिलता है?
If the areas of squares with sides (a+b) and (a-b) are subtracted, which area is obtained visually?
#difference of two squares
#area comparison
#visual model
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A (2ab)
B (4ab)
C \(a^2+b^2\)
D \(a^2-b^2\)
Explanation opens after your attempt
Step 1
Concept
((a+b)2 -(a-b)2 =4ab). Exam tip: compare the middle terms of both squares.
Step 2
Why this answer is correct
The correct answer is B. (4ab). ((a+b)2 -(a-b)2 =4ab). Exam tip: compare the middle terms of both squares.
Step 3
Exam Tip
((a+b)2 -(a-b)2 =4ab) होता है। परीक्षा में दोनों वर्गों के मध्य पदों का अंतर देखें।
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एक मॉडल में \(x^2-2xy+y^2\) का वर्ग दिखता है। इसे किस बाहरी भुजा से जोड़ा जाएगा?
A model shows the square \(x^2-2xy+y^2\). With which outer side will it be connected?
#square of difference
#outer side
#visual identity
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A (x+y)
B (x-2y)
C (x-y)
D (2x-y)
Explanation opens after your attempt
Step 1
Concept
This is the expansion of ((x-y)2 ). Exam tip: identify (x-y) in the side from (-2xy).
Step 2
Why this answer is correct
The correct answer is C. (x-y). This is the expansion of ((x-y)2 ). Exam tip: identify (x-y) in the side from (-2xy).
Step 3
Exam Tip
यह ((x-y)2 ) का विस्तार है। परीक्षा में (-2xy) देखकर भुजा में (x-y) पहचानें।
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यदि किसी वर्ग मॉडल में \(x^2\) और (64) कोने के वर्ग हैं, तो पूर्ण वर्ग बनने के लिए बीच का संयुक्त पद क्या होना चाहिए?
If a square model has corner squares \(x^2\) and (64), what combined middle term is needed to form a perfect square?
#complete square
#missing middle
#area tiles
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A (8x)
B (16x)
C (32x)
D (64x)
Explanation opens after your attempt
Step 1
Concept
Since \(64=8^2\), the combined middle term is \(2\cdot x\cdot 8=16x\). Exam tip: get side (8) from the corner square.
Step 2
Why this answer is correct
The correct answer is B. (16x). Since \(64=8^2\), the combined middle term is \(2\cdot x\cdot 8=16x\). Exam tip: get side (8) from the corner square.
Step 3
Exam Tip
\(64=8^2\) है इसलिए संयुक्त मध्य पद \(2\cdot x\cdot 8=16x\) होगा। परीक्षा में कोने के वर्ग से भुजा (8) निकालें।
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भुजाएँ (x+y) और (x-y) वाले आयत को क्षेत्रफल मॉडल में फैलाने पर (xy) पद क्यों नहीं बचता?
Why does the (xy) term not remain when a rectangle with sides (x+y) and (x-y) is expanded in an area model?
#cancellation
#xy terms
#rectangle model
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A क्योंकि (xy) और (-xy) पद कट जाते हैं / Because (xy) and (-xy) terms cancel
B क्योंकि (xy) का क्षेत्रफल बनता ही नहीं / Because no (xy) area is formed
C क्योंकि \(x^2\) शून्य हो जाता है / Because \(x^2\) becomes zero
D क्योंकि \(y^2\) धनात्मक हो जाता है / Because \(y^2\) becomes positive
Explanation opens after your attempt
Correct Answer
A. क्योंकि (xy) और (-xy) पद कट जाते हैं / Because (xy) and (-xy) terms cancel
Step 1
Concept
In the four parts, (xy) and (-xy) cancel each other. Exam tip: middle terms cancel in the sum-and-difference model.
Step 2
Why this answer is correct
The correct answer is A. क्योंकि (xy) और (-xy) पद कट जाते हैं / Because (xy) and (-xy) terms cancel. In the four parts, (xy) and (-xy) cancel each other. Exam tip: middle terms cancel in the sum-and-difference model.
Step 3
Exam Tip
चार भागों में (xy) और (-xy) एक दूसरे को खत्म करते हैं। परीक्षा में योग और अंतर के मॉडल में मध्य पद कटते हैं।
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एक वर्ग मॉडल में \(m^2+2mn+n^2=196\) है। यदि बाहरी भुजा (m+n) धनात्मक है, तो (m+n) क्या होगा?
In a square model, \(m^2+2mn+n^2=196\). If the outer side (m+n) is positive, what is (m+n)?
#total square
#outer side
#visual identity
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A (14)
B (98)
C (28)
D (196)
Explanation opens after your attempt
Step 1
Concept
(m-2 +2mn+n-2 =(m+n)2 ) and the square root of (196) is (14). Exam tip: take the square root of the whole model.
Step 2
Why this answer is correct
The correct answer is A. (14). (m-2 +2mn+n-2 =(m+n)2 ) and the square root of (196) is (14). Exam tip: take the square root of the whole model.
Step 3
Exam Tip
(m-2 +2mn+n-2 =(m+n)2 ) है और (196) का वर्गमूल (14) है। परीक्षा में पूरे मॉडल का वर्गमूल लें।
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यदि आयत मॉडल में ((x-6)(x+2)) है, तो (x) वाले पदों का संयुक्त चिन्ह और मान क्या होगा?
If a rectangle model represents ((x-6)(x+2)), what is the sign and value of the combined (x)-term?
#signed rectangles
#area model
#like terms
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A धनात्मक (8x) / Positive (8x)
B ऋणात्मक (4x) / Negative (4x)
C धनात्मक (4x) / Positive (4x)
D ऋणात्मक (8x) / Negative (8x)
Explanation opens after your attempt
Correct Answer
B. ऋणात्मक (4x) / Negative (4x)
Step 1
Concept
The sum of (2x) and (-6x) is (-4x). Exam tip: watch signs when adding positive and negative rectangles.
Step 2
Why this answer is correct
The correct answer is B. ऋणात्मक (4x) / Negative (4x). The sum of (2x) and (-6x) is (-4x). Exam tip: watch signs when adding positive and negative rectangles.
Step 3
Exam Tip
(2x) और (-6x) का योग (-4x) है। परीक्षा में धन और ऋण आयतों को जोड़ते समय चिन्ह देखें।
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यदि \(9x^2-25y^2\) का दृश्य मॉडल बनाया जाए, तो कटकर बने आयत की भुजाएँ कौन सी होंगी?
If a visual model of \(9x^2-25y^2\) is made, what will be the sides of the rearranged rectangle?
#difference of squares
#rearranged rectangle
#visual factor
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A (3x+5y) और (3x-5y) / (3x+5y) and (3x-5y)
B (9x+25y) और (9x-25y) / (9x+25y) and (9x-25y)
C (3x) और (5y) / (3x) and (5y)
D \(9x^2\) और \(25y^2\) / \(9x^2\) and \(25y^2\)
Explanation opens after your attempt
Correct Answer
A. (3x+5y) और (3x-5y) / (3x+5y) and (3x-5y)
Step 1
Concept
(9x-2 =(3x)2 ) and (25y-2 =(5y)2 ). Exam tip: first find the sides of both squares.
Step 2
Why this answer is correct
The correct answer is A. (3x+5y) और (3x-5y) / (3x+5y) and (3x-5y). (9x-2 =(3x)2 ) and (25y-2 =(5y)2 ). Exam tip: first find the sides of both squares.
Step 3
Exam Tip
(9x-2 =(3x)2 ) और (25y-2 =(5y)2 ) है। परीक्षा में पहले दोनों वर्गों की भुजाएँ निकालें।
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एक वर्ग के अंदर \(x^2\) और (81) कोने दिखते हैं। यदि पूरा क्षेत्रफल \(x^2-18x+81\) है, तो मॉडल किस भुजा का है?
Inside a square, corner parts \(x^2\) and (81) are shown. If the total area is \(x^2-18x+81\), what is the side of the model?
#negative square
#corner square
#visual model
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A (x+9)
B (x-18)
C (x-9)
D (x+18)
Explanation opens after your attempt
Step 1
Concept
\(81=9^2\) and the middle term is (-18x), so the side is (x-9). Exam tip: get the number from last term and sign from middle term.
Step 2
Why this answer is correct
The correct answer is C. (x-9). \(81=9^2\) and the middle term is (-18x), so the side is (x-9). Exam tip: get the number from last term and sign from middle term.
Step 3
Exam Tip
\(81=9^2\) और मध्य पद (-18x) है इसलिए भुजा (x-9) है। परीक्षा में अंतिम पद से संख्या और मध्य पद से चिन्ह लें।
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यदि दो वर्गों के क्षेत्रफल (121) और (49) हैं, तो उनके अंतर के दृश्य आयत का क्षेत्रफल क्या होगा?
If the areas of two squares are (121) and (49), what is the area of the visual rectangle for their difference?
#numeric squares
#difference model
#area
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A (72)
B (84)
C (170)
D (35)
Explanation opens after your attempt
Step 1
Concept
The bigger area is (121) and the smaller is (49), so the difference is (72). Exam tip: subtract the square areas first.
Step 2
Why this answer is correct
The correct answer is A. (72). The bigger area is (121) and the smaller is (49), so the difference is (72). Exam tip: subtract the square areas first.
Step 3
Exam Tip
बड़ा क्षेत्रफल (121) और छोटा (49) है इसलिए अंतर (72) है। परीक्षा में पहले वर्गों के क्षेत्रफल घटाएँ।
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एक आयत मॉडल में कुल क्षेत्रफल \(2x^2+11x+12\) है। यदि एक भुजा (2x+3) है, तो दूसरी भुजा कौन सी होगी?
A rectangle model has total area \(2x^2+11x+12\). If one side is (2x+3), what is the other side?
#unknown side
#rectangle factor
#area split
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A (x+3)
B (x+4)
C (2x+4)
D (x+8)
Explanation opens after your attempt
Step 1
Concept
((2x+3)(x+4)=2x-2 +8x+3x+12=2x-2 +11x+12). Exam tip: check the sum of middle terms.
Step 2
Why this answer is correct
The correct answer is B. (x+4). ((2x+3)(x+4)=2x-2 +8x+3x+12=2x-2 +11x+12). Exam tip: check the sum of middle terms.
Step 3
Exam Tip
((2x+3)(x+4)=2x-2 +8x+3x+12=2x-2 +11x+12)। परीक्षा में मध्य पदों का योग जाँचें।
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यदि ((a+b)2 ) के मॉडल में \(a^2=64\), \(b^2=36\) और दोनों धनात्मक हैं, तो (2ab) वाला संयुक्त आयत क्षेत्रफल कितना होगा?
If in the model of ((a+b)2 ), \(a^2=64\), \(b^2=36\), and both are positive, what is the combined rectangular area (2ab)?
#square areas
#rectangular middle
#visual identity
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A (100)
B (48)
C (96)
D (28)
Explanation opens after your attempt
Step 1
Concept
(a=8) and (b=6), so (2ab=96). Exam tip: find side lengths from square areas and add rectangle areas.
Step 2
Why this answer is correct
The correct answer is C. (96). (a=8) and (b=6), so (2ab=96). Exam tip: find side lengths from square areas and add rectangle areas.
Step 3
Exam Tip
(a=8) और (b=6), इसलिए (2ab=96) है। परीक्षा में वर्ग क्षेत्रफल से भुजा निकालकर आयत क्षेत्रफल जोड़ें।
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एक दृश्य मॉडल में ((x+y)2 ), ((x-y)2 ) और (4xy) तीन क्षेत्र दिखाए गए हैं। सही संबंध कौन सा है?
A visual model shows three areas ((x+y)2 ), ((x-y)2 ), and (4xy). Which relation is correct?
#area relation
#two squares
#visual comparison
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A ((x+y)2 =(x-y)2 +4xy)
B ((x-y)2 =(x+y)2 +4xy)
C (4xy=(x+y)2 +(x-y)2 )
D ((x+y)2 =(x-y)2 -4xy)
Explanation opens after your attempt
Correct Answer
A. ((x+y)2 =(x-y)2 +4xy)
Step 1
Concept
Since ((x+y)2 -(x-y)2 =4xy), the first square is greater than the second by (4xy). Exam tip: remember the difference of these two squares.
Step 2
Why this answer is correct
The correct answer is A. ((x+y)2 =(x-y)2 +4xy). Since ((x+y)2 -(x-y)2 =4xy), the first square is greater than the second by (4xy). Exam tip: remember the difference of these two squares.
Step 3
Exam Tip
क्योंकि ((x+y)2 -(x-y)2 =4xy), इसलिए पहला वर्ग दूसरे से (4xy) अधिक है। परीक्षा में दोनों वर्गों का अंतर याद रखें।
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