क्षेत्रफल मॉडल में एक बड़ा वर्ग दो भागों (a) और (b) से बना है। पूरे वर्ग का क्षेत्रफल कौन सा होगा?
In an area model, a big square is made with two parts (a) and (b). What is the area of the whole square?
#algebraic identities
#area model
#square
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A \(a^2+2ab+b^2\)
B \(a^2-b^2\)
C \(a^2+b^2\)
D (2a+2b)
Explanation opens after your attempt
Correct Answer
A. \(a^2+2ab+b^2\)
Step 1
Concept
The side of the square is (a+b), so area is ((a+b)2 ). Exam tip: identify the side of the square first.
Step 2
Why this answer is correct
The correct answer is A. \(a^2+2ab+b^2\). The side of the square is (a+b), so area is ((a+b)2 ). Exam tip: identify the side of the square first.
Step 3
Exam Tip
वर्ग की भुजा (a+b) है इसलिए क्षेत्रफल ((a+b)2 ) होता है। परीक्षा में वर्ग की भुजा पहले पहचानें।
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यदि वर्ग मॉडल में भुजा (x+3) हो तो उसका विस्तृत क्षेत्रफल क्या होगा?
If the side of a square model is (x+3), what is its expanded area?
#visual model
#binomial square
#area
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A \(x^2+3x+9\)
B \(x^2+6x+9\)
C \(x^2+9x+6\)
D \(x^2-6x+9\)
Explanation opens after your attempt
Correct Answer
B. \(x^2+6x+9\)
Step 1
Concept
In ((x+3)2 ), the middle term is \(2\cdot x\cdot 3\). Exam tip: do not forget the two equal rectangles.
Step 2
Why this answer is correct
The correct answer is B. \(x^2+6x+9\). In ((x+3)2 ), the middle term is \(2\cdot x\cdot 3\). Exam tip: do not forget the two equal rectangles.
Step 3
Exam Tip
((x+3)2 ) में बीच का पद \(2\cdot x\cdot 3\) होता है। परीक्षा में दो समान आयतों को जोड़ना न भूलें।
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एक क्षेत्रफल चित्र में बड़े वर्ग से (b) चौड़ाई की पट्टी हटाई गई है। यह कौन सी पहचान दिखाता है?
In an area diagram, a strip of width (b) is removed from a big square. Which identity does this show?
#subtraction model
#square identity
#visual algebra
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A ((a+b)2 =a-2 +2ab+b-2 )
B (a-2 -b-2 =(a+b)2 )
C ((a-b)2 =a-2 -2ab+b-2 )
D \(a^2+b^2=2ab\)
Explanation opens after your attempt
Correct Answer
C. ((a-b)2 =a-2 -2ab+b-2 )
Step 1
Concept
In a removal model, the remaining side is (a-b). Exam tip: connect the subtraction square with ((a-b)2 ).
Step 2
Why this answer is correct
The correct answer is C. ((a-b)2 =a-2 -2ab+b-2 ). In a removal model, the remaining side is (a-b). Exam tip: connect the subtraction square with ((a-b)2 ).
Step 3
Exam Tip
हटाने वाले मॉडल में बची भुजा (a-b) होती है। परीक्षा में घटाव वाले वर्ग को ((a-b)2 ) से जोड़ें।
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भुजाओं (a+b) और (a-b) वाले आयत का क्षेत्रफल किसके बराबर है?
The area of a rectangle with sides (a+b) and (a-b) is equal to what?
#rectangle model
#difference of squares
#area
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A \(a^2+2ab+b^2\)
B \(a^2+ab-b^2\)
C \(a^2+b^2\)
D \(a^2-b^2\)
Explanation opens after your attempt
Correct Answer
D. \(a^2-b^2\)
Step 1
Concept
The area is ((a+b)(a-b)), which becomes \(a^2-b^2\). Exam tip: remember product of sum and difference.
Step 2
Why this answer is correct
The correct answer is D. \(a^2-b^2\). The area is ((a+b)(a-b)), which becomes \(a^2-b^2\). Exam tip: remember product of sum and difference.
Step 3
Exam Tip
क्षेत्रफल ((a+b)(a-b)) है जो \(a^2-b^2\) बनता है। परीक्षा में योग और अंतर का गुणन याद रखें।
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टाइल मॉडल में \(x^2\) की एक टाइल, (x) की चार टाइलें और (1) की चार टाइलें मिलकर कौन सा वर्ग बनाते हैं?
In a tile model, one \(x^2\) tile, four (x) tiles, and four unit tiles form which square?
#algebra tiles
#perfect square
#visual model
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A ((x+2)2 )
B ((x+4)2 )
C \(x^2+2x+4\)
D ((x-2)2 )
Explanation opens after your attempt
Correct Answer
A. ((x+2)2 )
Step 1
Concept
The total area is \(x^2+4x+4\), which is ((x+2)2 ). Exam tip: identify the number from unit tiles.
Step 2
Why this answer is correct
The correct answer is A. ((x+2)2 ). The total area is \(x^2+4x+4\), which is ((x+2)2 ). Exam tip: identify the number from unit tiles.
Step 3
Exam Tip
कुल क्षेत्रफल \(x^2+4x+4\) है जो ((x+2)2 ) है। परीक्षा में इकाई टाइलों से संख्या पहचानें।
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भुजा (p+q) वाले वर्ग को चार क्षेत्रों में बाँटा गया है। दो आयतों का संयुक्त क्षेत्रफल क्या होगा?
A square of side (p+q) is divided into four regions. What is the combined area of the two rectangles?
#area split
#rectangle parts
#identity
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A \(p^2+q^2\)
B (2pq)
C (pq)
D (p+q)
Explanation opens after your attempt
Step 1
Concept
The two rectangles have areas (pq) and (pq). So their sum is (2pq).
Step 2
Why this answer is correct
The correct answer is B. (2pq). The two rectangles have areas (pq) and (pq). So their sum is (2pq).
Step 3
Exam Tip
दोनों आयतों का क्षेत्रफल (pq) और (pq) है। इसलिए उनका योग (2pq) होगा।
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चित्र में (m+n) भुजा वाला वर्ग \(m^2\), (mn), (mn), \(n^2\) भागों में है। कुल क्षेत्रफल कौन सा है?
A square of side (m+n) is shown with parts \(m^2\), (mn), (mn), and \(n^2\). What is the total area?
#square partition
#area addition
#visual identity
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A \(m^2+mn+n^2\)
B \(m^2+n^2\)
C \(m^2+2mn+n^2\)
D \(2m^2+2n^2\)
Explanation opens after your attempt
Correct Answer
C. \(m^2+2mn+n^2\)
Step 1
Concept
Adding the four parts gives \(m^2+2mn+n^2\). Exam tip: combine the equal (mn) parts.
Step 2
Why this answer is correct
The correct answer is C. \(m^2+2mn+n^2\). Adding the four parts gives \(m^2+2mn+n^2\). Exam tip: combine the equal (mn) parts.
Step 3
Exam Tip
चारों भागों को जोड़ने पर \(m^2+2mn+n^2\) मिलता है। परीक्षा में समान (mn) भागों को साथ जोड़ें।
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यदि दृश्य मॉडल में बड़े वर्ग का क्षेत्रफल \(a^2\) है और छोटे कोने का क्षेत्रफल \(b^2\) हटता है, तो शेष से कौन सा गुणनफल बनता है?
If a visual model has a big square of area \(a^2\) and a small corner of area \(b^2\) removed, which product can represent the remaining area after rearrangement?
#difference of squares
#cut model
#rearrangement
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A ((a+b)2 )
B (a(a+b))
C (b(a-b))
D ((a+b)(a-b))
Explanation opens after your attempt
Correct Answer
D. ((a+b)(a-b))
Step 1
Concept
The remaining area is \(a^2-b^2\), which equals ((a+b)(a-b)). Exam tip: understand the cut-and-rearrange model.
Step 2
Why this answer is correct
The correct answer is D. ((a+b)(a-b)). The remaining area is \(a^2-b^2\), which equals ((a+b)(a-b)). Exam tip: understand the cut-and-rearrange model.
Step 3
Exam Tip
शेष क्षेत्रफल \(a^2-b^2\) है और यह ((a+b)(a-b)) के बराबर है। परीक्षा में काटकर जोड़ने वाले मॉडल को समझें।
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वर्ग की भुजा (y+5) है। क्षेत्रफल मॉडल के अनुसार बीच का पद क्या होगा?
The side of a square is (y+5). According to the area model, what will be the middle term?
#middle term
#area model
#binomial square
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A (10y)
B (5y)
C (25y)
D \(y^2\)
Explanation opens after your attempt
Step 1
Concept
The middle term is \(2\cdot y\cdot 5=10y\). Exam tip: focus on (2ab) in ((a+b)2 ).
Step 2
Why this answer is correct
The correct answer is A. (10y). The middle term is \(2\cdot y\cdot 5=10y\). Exam tip: focus on (2ab) in ((a+b)2 ).
Step 3
Exam Tip
बीच का पद \(2\cdot y\cdot 5=10y\) है। परीक्षा में ((a+b)2 ) में (2ab) पर ध्यान दें।
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टाइलों से \(x^2+8x+16\) का वर्ग बनाया गया है। इसकी भुजा क्या होगी?
A square is made from tiles representing \(x^2+8x+16\). What will be its side?
#tiles
#perfect square
#side length
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A (x+8)
B (x+4)
C (x+16)
D (x-4)
Explanation opens after your attempt
Step 1
Concept
Taking (16) as \(4^2\), the middle term is \(2\cdot x\cdot 4=8x\). Exam tip: check the square root of the constant term.
Step 2
Why this answer is correct
The correct answer is B. (x+4). Taking (16) as \(4^2\), the middle term is \(2\cdot x\cdot 4=8x\). Exam tip: check the square root of the constant term.
Step 3
Exam Tip
(16) को \(4^2\) मानने पर बीच का पद \(2\cdot x\cdot 4=8x\) है। परीक्षा में स्थिर पद का वर्गमूल देखें।
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एक आयत मॉडल में लंबाई (r+2) और चौड़ाई (r+3) है। कुल क्षेत्रफल कौन सा होगा?
In a rectangle model, the length is (r+2) and the breadth is (r+3). What is the total area?
#rectangle area
#visual multiplication
#identity
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A \(r^2+6\)
B \(r^2+2r+3r\)
C \(r^2+5r+6\)
D \(r^2+6r+5\)
Explanation opens after your attempt
Correct Answer
C. \(r^2+5r+6\)
Step 1
Concept
The area is ((r+2)(r+3)), which becomes \(r^2+5r+6\). Exam tip: add the four parts of the rectangle.
Step 2
Why this answer is correct
The correct answer is C. \(r^2+5r+6\). The area is ((r+2)(r+3)), which becomes \(r^2+5r+6\). Exam tip: add the four parts of the rectangle.
Step 3
Exam Tip
क्षेत्रफल ((r+2)(r+3)) है जो \(r^2+5r+6\) बनता है। परीक्षा में आयत के चार भाग जोड़ें।
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भुजा (a-b) वाले वर्ग के दृश्य मॉडल में कौन सा क्षेत्रफल जोड़कर पूरा \(a^2\) वर्ग बनता है?
In the visual model of a square with side (a-b), which areas are added to complete the \(a^2\) square?
#subtraction square
#area completion
#identity
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A \(b^2\) केवल / \(b^2\) only
B (ab) केवल / (ab) only
C (2a) केवल / (2a) only
D \(2ab-b^2\)
Explanation opens after your attempt
Correct Answer
D. \(2ab-b^2\)
Step 1
Concept
Since ((a-b)2 =a-2 -2ab+b-2 ), the missing part relates to \(2ab-b^2\). Exam tip: read the removed part carefully.
Step 2
Why this answer is correct
The correct answer is D. \(2ab-b^2\). Since ((a-b)2 =a-2 -2ab+b-2 ), the missing part relates to \(2ab-b^2\). Exam tip: read the removed part carefully.
Step 3
Exam Tip
((a-b)2 =a-2 -2ab+b-2 ) इसलिए शेष जोड़ \(2ab-b^2\) से जुड़ता है। परीक्षा में घटे हुए भाग को ध्यान से पढ़ें।
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यदि वर्ग मॉडल में भुजा (2x+1) है तो क्षेत्रफल का विस्तार क्या होगा?
If the side of a square model is (2x+1), what is the expansion of its area?
#square model
#binomial identity
#expansion
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A \(4x^2+4x+1\)
B \(2x^2+2x+1\)
C \(4x^2+1\)
D \(4x^2+2x+1\)
Explanation opens after your attempt
Correct Answer
A. \(4x^2+4x+1\)
Step 1
Concept
In ((2x+1)2 ), \(2\cdot 2x\cdot 1=4x\) appears. Exam tip: write the square of the first term as \(4x^2\).
Step 2
Why this answer is correct
The correct answer is A. \(4x^2+4x+1\). In ((2x+1)2 ), \(2\cdot 2x\cdot 1=4x\) appears. Exam tip: write the square of the first term as \(4x^2\).
Step 3
Exam Tip
((2x+1)2 ) में \(2\cdot 2x\cdot 1=4x\) आता है। परीक्षा में पहले पद का वर्ग \(4x^2\) लिखें।
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क्षेत्रफल चित्र में \(a^2-b^2\) को आयत में बदलने पर आयत की भुजाएँ क्या होंगी?
When \(a^2-b^2\) is changed into a rectangle in an area diagram, what are the sides of the rectangle?
#difference of squares
#rectangle sides
#visual proof
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A (a) और (b) / (a) and (b)
B (a+b) और (a-b) / (a+b) and (a-b)
C \(a^2\) और \(b^2\) / \(a^2\) and \(b^2\)
D (2a) और (2b) / (2a) and (2b)
Explanation opens after your attempt
Correct Answer
B. (a+b) और (a-b) / (a+b) and (a-b)
Step 1
Concept
In the difference of squares model, the rectangle sides are sum and difference. Exam tip: connect \(a^2-b^2\) with ((a+b)(a-b)).
Step 2
Why this answer is correct
The correct answer is B. (a+b) और (a-b) / (a+b) and (a-b). In the difference of squares model, the rectangle sides are sum and difference. Exam tip: connect \(a^2-b^2\) with ((a+b)(a-b)).
Step 3
Exam Tip
अंतर के वर्ग मॉडल में आयत की भुजाएँ योग और अंतर होती हैं। परीक्षा में \(a^2-b^2\) को ((a+b)(a-b)) से जोड़ें।
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भुजा (k-4) वाले वर्ग का क्षेत्रफल मॉडल कौन सा विस्तार देता है?
Which expansion is given by the area model of a square with side (k-4)?
#area model
#minus square
#identity
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A \(k^2-4k+16\)
B \(k^2+8k+16\)
C \(k^2-8k+16\)
D \(k^2-16\)
Explanation opens after your attempt
Correct Answer
C. \(k^2-8k+16\)
Step 1
Concept
((k-4)2 =k-2 -8k+16). Exam tip: keep the middle term negative in a subtraction square.
Step 2
Why this answer is correct
The correct answer is C. \(k^2-8k+16\). ((k-4)2 =k-2 -8k+16). Exam tip: keep the middle term negative in a subtraction square.
Step 3
Exam Tip
((k-4)2 =k-2 -8k+16) होता है। परीक्षा में घटाव वाले वर्ग में बीच का पद ऋणात्मक रखें।
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वर्ग मॉडल में \(a^2\), (2ab) और \(b^2\) तीन प्रकार के भाग दिखते हैं। यह किस पहचान का दृश्य प्रमाण है?
A square model shows three types of parts \(a^2\), (2ab), and \(b^2\). This is the visual proof of which identity?
#visual proof
#binomial square
#area parts
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A (a-2 -b-2 =(a+b)(a-b))
B (a-2 +b-2 =(a+b)2 )
C (a-2 -ab+b-2 =(a-b)2 )
D ((a+b)2 =a-2 +2ab+b-2 )
Explanation opens after your attempt
Correct Answer
D. ((a+b)2 =a-2 +2ab+b-2 )
Step 1
Concept
A square of side (a+b) is divided into these three parts. Exam tip: write the identity by adding areas.
Step 2
Why this answer is correct
The correct answer is D. ((a+b)2 =a-2 +2ab+b-2 ). A square of side (a+b) is divided into these three parts. Exam tip: write the identity by adding areas.
Step 3
Exam Tip
भुजा (a+b) वाला वर्ग इन तीन भागों में बंटता है। परीक्षा में क्षेत्रफल जोड़कर पहचान लिखें।
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(x+1) भुजा वाले वर्ग में कितनी (x) वाली आयत टाइलें आती हैं?
How many (x)-rectangle tiles appear in a square with side (x+1)?
#algebra tiles
#x tiles
#visual square
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A (2)
B (1)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
In ((x+1)2 =x-2 +2x+1), there are two (x)-rectangle tiles. Exam tip: count rectangles in both directions.
Step 2
Why this answer is correct
The correct answer is A. (2). In ((x+1)2 =x-2 +2x+1), there are two (x)-rectangle tiles. Exam tip: count rectangles in both directions.
Step 3
Exam Tip
((x+1)2 =x-2 +2x+1) में (x) वाली दो आयतें होती हैं। परीक्षा में दोनों दिशाओं की आयतें गिनें।
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आयत मॉडल में ((x+4)(x+1)) को चार भागों में बाँटने पर (x) वाले पदों का योग क्या है?
In a rectangle model for ((x+4)(x+1)), what is the sum of the (x)-terms after splitting into four parts?
#rectangle split
#like terms
#area model
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A (4x)
B (5x)
C \(x^2\)
D (4)
Explanation opens after your attempt
Step 1
Concept
The parts (4x) and (x) combine to make (5x). Exam tip: add like terms.
Step 2
Why this answer is correct
The correct answer is B. (5x). The parts (4x) and (x) combine to make (5x). Exam tip: add like terms.
Step 3
Exam Tip
भाग (4x) और (x) मिलकर (5x) बनाते हैं। परीक्षा में जैसे पदों को जोड़ें।
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किस दृश्य मॉडल में \(a^2\) वर्ग से \(b^2\) वर्ग हटाकर बाकी भाग को आयत बनाया जाता है?
In which visual model is a \(b^2\) square removed from an \(a^2\) square and the remaining part rearranged into a rectangle?
#visual rearrangement
#difference of squares
#area
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A ((a+b)2 )
B ((a-b)2 )
C \(a^2-b^2\)
D \(a^2+b^2\)
Explanation opens after your attempt
Correct Answer
C. \(a^2-b^2\)
Step 1
Concept
This is the difference of squares model. Exam tip: treat the removed small square as \(b^2\).
Step 2
Why this answer is correct
The correct answer is C. \(a^2-b^2\). This is the difference of squares model. Exam tip: treat the removed small square as \(b^2\).
Step 3
Exam Tip
यह अंतर के वर्ग का मॉडल है। परीक्षा में हटाए गए छोटे वर्ग को \(b^2\) मानें।
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भुजा (3x+2) वाले वर्ग में \(x^2\) वाले भाग का क्षेत्रफल क्या होगा?
In a square with side (3x+2), what is the area of the \(x^2\)-part?
#coefficient square
#area model
#binomial
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A \(3x^2\)
B \(6x^2\)
C \(2x^2\)
D \(9x^2\)
Explanation opens after your attempt
Correct Answer
D. \(9x^2\)
Step 1
Concept
The square of the first part (3x) is \(9x^2\). Exam tip: square the coefficient too.
Step 2
Why this answer is correct
The correct answer is D. \(9x^2\). The square of the first part (3x) is \(9x^2\). Exam tip: square the coefficient too.
Step 3
Exam Tip
पहले भाग (3x) का वर्ग \(9x^2\) होता है। परीक्षा में गुणांक का भी वर्ग करें।
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वर्गाकार टाइल मॉडल में \(z^2+6z+9\) दिखाया गया है। पूरा वर्ग किस भुजा का है?
A square tile model shows \(z^2+6z+9\). What is the side of the complete square?
#perfect square
#tile model
#side
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A (z+3)
B (z+6)
C (z+9)
D (z-3)
Explanation opens after your attempt
Step 1
Concept
Since \(9=3^2\) and the middle term is (6z), the side is (z+3). Exam tip: identify the smaller side from the last term.
Step 2
Why this answer is correct
The correct answer is A. (z+3). Since \(9=3^2\) and the middle term is (6z), the side is (z+3). Exam tip: identify the smaller side from the last term.
Step 3
Exam Tip
\(9=3^2\) और बीच का पद (6z) है इसलिए भुजा (z+3) है। परीक्षा में अंतिम पद से छोटी भुजा पहचानें।
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एक आयत की लंबाई (a+5) और चौड़ाई (a-5) है। दृश्य मॉडल किस क्षेत्रफल को दिखाता है?
A rectangle has length (a+5) and breadth (a-5). Which area does the visual model show?
#sum difference
#rectangle model
#identity
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A \(a^2+25\)
B \(a^2-25\)
C \(a^2-10a+25\)
D \(a^2+10a+25\)
Explanation opens after your attempt
Correct Answer
B. \(a^2-25\)
Step 1
Concept
((a+5)(a-5)=a-2 -25). Exam tip: identify the sum and difference of the same number.
Step 2
Why this answer is correct
The correct answer is B. \(a^2-25\). ((a+5)(a-5)=a-2 -25). Exam tip: identify the sum and difference of the same number.
Step 3
Exam Tip
((a+5)(a-5)=a-2 -25) होता है। परीक्षा में समान संख्या के योग और अंतर को पहचानें।
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यदि क्षेत्रफल मॉडल में दो समान आयतों का क्षेत्रफल (7x) और (7x) है, तो बीच का कुल पद क्या होगा?
If two equal rectangles in an area model have areas (7x) and (7x), what is the total middle term?
#middle rectangles
#area addition
#visual model
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A (7x)
B (49x)
C (14x)
D \(x^2\)
Explanation opens after your attempt
Step 1
Concept
The sum of the two equal rectangles is (7x+7x=14x). Exam tip: do not leave equal rectangles separate.
Step 2
Why this answer is correct
The correct answer is C. (14x). The sum of the two equal rectangles is (7x+7x=14x). Exam tip: do not leave equal rectangles separate.
Step 3
Exam Tip
दो समान आयतों का योग (7x+7x=14x) है। परीक्षा में समान आयतों को अलग अलग न छोड़ें।
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भुजा (x-1) वाले वर्ग के मॉडल में \(x^2\) के बाद बीच का पद कैसा होगा?
In the model of a square with side (x-1), what will the middle term after \(x^2\) be like?
#minus square
#middle term
#sign
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A धनात्मक (2x) / Positive (2x)
B धनात्मक (x) / Positive (x)
C शून्य / Zero
D ऋणात्मक (2x) / Negative (2x)
Explanation opens after your attempt
Correct Answer
D. ऋणात्मक (2x) / Negative (2x)
Step 1
Concept
In ((x-1)2 =x-2 -2x+1), the middle term is negative. Exam tip: keep the negative sign safe.
Step 2
Why this answer is correct
The correct answer is D. ऋणात्मक (2x) / Negative (2x). In ((x-1)2 =x-2 -2x+1), the middle term is negative. Exam tip: keep the negative sign safe.
Step 3
Exam Tip
((x-1)2 =x-2 -2x+1) में बीच का पद ऋणात्मक होता है। परीक्षा में ऋण चिह्न को सुरक्षित रखें।
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एक वर्ग मॉडल में \(x^2\), (12x) और (36) भाग दिखते हैं। यह किस वर्ग की भुजा बताता है?
A square model shows parts \(x^2\), (12x), and (36). What side of the square does it indicate?
#perfect square
#area parts
#visual identity
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A (x+6)
B (x+12)
C (x+36)
D (x-6)
Explanation opens after your attempt
Step 1
Concept
\(36=6^2\) and \(2\cdot x\cdot 6=12x\). Exam tip: check the perfect square pattern.
Step 2
Why this answer is correct
The correct answer is A. (x+6). \(36=6^2\) and \(2\cdot x\cdot 6=12x\). Exam tip: check the perfect square pattern.
Step 3
Exam Tip
\(36=6^2\) और \(2\cdot x\cdot 6=12x\) है। परीक्षा में पूर्ण वर्ग की जाँच करें।
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आयत मॉडल में ((p+2)(p+5)) के कोने वाले छोटे आयत का क्षेत्रफल क्या है?
In the rectangle model of ((p+2)(p+5)), what is the area of the small corner rectangle?
#rectangle corner
#area multiplication
#visual algebra
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A (2p)
B (10)
C (5p)
D (7p)
Explanation opens after your attempt
Step 1
Concept
The small corner area is \(2\cdot 5=10\). Exam tip: multiply the numerical parts.
Step 2
Why this answer is correct
The correct answer is B. (10). The small corner area is \(2\cdot 5=10\). Exam tip: multiply the numerical parts.
Step 3
Exam Tip
छोटे कोने का क्षेत्रफल \(2\cdot 5=10\) है। परीक्षा में संख्यात्मक भागों का गुणन करें।
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भुजा (a+2b) वाले वर्ग का क्षेत्रफल मॉडल कौन सा विस्तार देता है?
Which expansion is given by the area model of a square with side (a+2b)?
#binomial square
#area model
#algebraic identity
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A \(a^2+2ab+4b^2\)
B \(a^2+4b^2\)
C \(a^2+4ab+4b^2\)
D \(a^2+2ab+2b^2\)
Explanation opens after your attempt
Correct Answer
C. \(a^2+4ab+4b^2\)
Step 1
Concept
In ((a+2b)2 ), the middle term is \(2\cdot a\cdot 2b=4ab\). Exam tip: write the square of the second term as \(4b^2\).
Step 2
Why this answer is correct
The correct answer is C. \(a^2+4ab+4b^2\). In ((a+2b)2 ), the middle term is \(2\cdot a\cdot 2b=4ab\). Exam tip: write the square of the second term as \(4b^2\).
Step 3
Exam Tip
((a+2b)2 ) में बीच का पद \(2\cdot a\cdot 2b=4ab\) है। परीक्षा में दूसरे पद का वर्ग \(4b^2\) लिखें।
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दृश्य मॉडल में \(c^2-d^2\) का आयत रूप किसके बराबर होता है?
In a visual model, the rectangular form of \(c^2-d^2\) is equal to what?
#difference of squares
#rectangular form
#visual proof
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A (c(c-d))
B (d(c+d))
C \(c^2+d^2\)
D ((c+d)(c-d))
Explanation opens after your attempt
Correct Answer
D. ((c+d)(c-d))
Step 1
Concept
\(c^2-d^2\) can be rearranged into a ((c+d)(c-d)) rectangle. Exam tip: identify the big and small squares.
Step 2
Why this answer is correct
The correct answer is D. ((c+d)(c-d)). \(c^2-d^2\) can be rearranged into a ((c+d)(c-d)) rectangle. Exam tip: identify the big and small squares.
Step 3
Exam Tip
\(c^2-d^2\) को काटकर ((c+d)(c-d)) आयत बनाया जा सकता है। परीक्षा में बड़ा वर्ग और छोटा वर्ग पहचानें।
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यदि वर्ग मॉडल में भुजा (n+7) है, तो छोटे कोने वाले वर्ग का क्षेत्रफल क्या होगा?
If the side of a square model is (n+7), what is the area of the small corner square?
#corner square
#area model
#constant term
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A (49)
B (7n)
C (14n)
D \(n^2\)
Explanation opens after your attempt
Step 1
Concept
The small corner side is (7), so its area is (49). Exam tip: square the constant part.
Step 2
Why this answer is correct
The correct answer is A. (49). The small corner side is (7), so its area is (49). Exam tip: square the constant part.
Step 3
Exam Tip
छोटे कोने की भुजा (7) है इसलिए क्षेत्रफल (49) है। परीक्षा में स्थिर भाग का वर्ग लें।
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भुजा (t-3) वाले वर्ग के मॉडल में अंतिम पद क्या होगा?
In the model of a square with side (t-3), what will be the last term?
#minus square
#last term
#area model
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A (-9)
B (9)
C (3t)
D (-6t)
Explanation opens after your attempt
Step 1
Concept
((-3)2 =9), so the last term is positive. Exam tip: the square of a negative number is positive.
Step 2
Why this answer is correct
The correct answer is B. (9). ((-3)2 =9), so the last term is positive. Exam tip: the square of a negative number is positive.
Step 3
Exam Tip
((-3)2 =9) होता है इसलिए अंतिम पद धनात्मक है। परीक्षा में ऋण संख्या का वर्ग धनात्मक होता है।
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एक क्षेत्रफल मॉडल में आयत के चार भाग \(u^2\), (2u), (5u), (10) हैं। पूरा आयत किस गुणनफल को दिखाता है?
In an area model, the four parts of a rectangle are \(u^2\), (2u), (5u), and (10). Which product does the whole rectangle show?
#area model
#factor form
#rectangle
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A ((u+10)(u+1))
B ((u+2)(u+2))
C ((u+2)(u+5))
D ((u+5)(u+5))
Explanation opens after your attempt
Correct Answer
C. ((u+2)(u+5))
Step 1
Concept
The parts (2u), (5u), and (10) show the numbers (2) and (5). Exam tip: match the numbers using the corner product.
Step 2
Why this answer is correct
The correct answer is C. ((u+2)(u+5)). The parts (2u), (5u), and (10) show the numbers (2) and (5). Exam tip: match the numbers using the corner product.
Step 3
Exam Tip
भाग (2u), (5u) और (10) से संख्याएँ (2) और (5) मिलती हैं। परीक्षा में कोने के गुणन से दोनों संख्याएँ मिलाएँ।
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वर्ग मॉडल में \(4x^2+12x+9\) दिखाई देता है। इसकी भुजा क्या होगी?
A square model shows \(4x^2+12x+9\). What will be its side?
#perfect square trinomial
#visual square
#side
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A (2x+9)
B (4x+3)
C (2x+6)
D (2x+3)
Explanation opens after your attempt
Step 1
Concept
(4x-2 =(2x)2 ) and \(9=3^2\), with middle term (12x). Exam tip: identify both square terms.
Step 2
Why this answer is correct
The correct answer is D. (2x+3). (4x-2 =(2x)2 ) and \(9=3^2\), with middle term (12x). Exam tip: identify both square terms.
Step 3
Exam Tip
(4x-2 =(2x)2 ) और \(9=3^2\), बीच का पद (12x) है। परीक्षा में दोनों वर्ग पद पहचानें।
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भुजा (a+b) वाले वर्ग में \(a^2\) भाग किस आकार का होता है?
In a square with side (a+b), what shape is the \(a^2\) part?
#square part
#area model
#visual identity
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A भुजा (a) वाला वर्ग / A square of side (a)
B भुजा (b) वाला वर्ग / A square of side (b)
C भुजाएँ (a) और (b) वाला आयत / A rectangle of sides (a) and (b)
D भुजा (a+b) वाला आयत / A rectangle of side (a+b)
Explanation opens after your attempt
Correct Answer
A. भुजा (a) वाला वर्ग / A square of side (a)
Step 1
Concept
\(a^2\) means the area of a square of side (a). Exam tip: keep the difference between area and side clear.
Step 2
Why this answer is correct
The correct answer is A. भुजा (a) वाला वर्ग / A square of side (a). \(a^2\) means the area of a square of side (a). Exam tip: keep the difference between area and side clear.
Step 3
Exam Tip
\(a^2\) का अर्थ भुजा (a) वाले वर्ग का क्षेत्रफल है। परीक्षा में क्षेत्रफल और भुजा में अंतर रखें।
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यदि एक वर्ग की भुजा (x+2) है, तो चार भागों में कौन सा भाग नहीं आएगा?
If the side of a square is (x+2), which part will not appear among its four regions?
#four parts
#square model
#non example
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A \(x^2\)
B (3x)
C (2x)
D (4)
Explanation opens after your attempt
Step 1
Concept
The parts of ((x+2)2 ) are \(x^2\), (2x), (2x), and (4). Exam tip: identify every part of the model separately.
Step 2
Why this answer is correct
The correct answer is B. (3x). The parts of ((x+2)2 ) are \(x^2\), (2x), (2x), and (4). Exam tip: identify every part of the model separately.
Step 3
Exam Tip
((x+2)2 ) के भाग \(x^2\), (2x), (2x), (4) हैं। परीक्षा में मॉडल के हर भाग को अलग पहचानें।
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दृश्य मॉडल में भुजा (a) वाले वर्ग से भुजा (b) वाला वर्ग हटाने पर बचा क्षेत्रफल क्या कहलाता है?
In a visual model, when a square of side (b) is removed from a square of side (a), what is the remaining area called?
#difference of squares
#visual removal
#area
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A योग का वर्ग / Square of sum
B पूर्ण वर्ग त्रिपद / Perfect square trinomial
C वर्गों का अंतर / Difference of squares
D दो वर्गों का योग / Sum of two squares
Explanation opens after your attempt
Correct Answer
C. वर्गों का अंतर / Difference of squares
Step 1
Concept
The remaining area is \(a^2-b^2\), called difference of squares. Exam tip: connect removal with subtraction.
Step 2
Why this answer is correct
The correct answer is C. वर्गों का अंतर / Difference of squares. The remaining area is \(a^2-b^2\), called difference of squares. Exam tip: connect removal with subtraction.
Step 3
Exam Tip
बचा क्षेत्रफल \(a^2-b^2\) है जिसे वर्गों का अंतर कहते हैं। परीक्षा में हटाने को घटाव से जोड़ें।
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आयत मॉडल में लंबाई (x+6) और चौड़ाई (x) है। क्षेत्रफल कौन सा होगा?
In a rectangle model, the length is (x+6) and the breadth is (x). What is the area?
#rectangle area
#distributive model
#visual algebra
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A \(x^2+6\)
B \(6x^2\)
C (x+6x)
D \(x^2+6x\)
Explanation opens after your attempt
Correct Answer
D. \(x^2+6x\)
Step 1
Concept
The area is (x(x+6)=x-2 +6x). Exam tip: use length times breadth for rectangle area.
Step 2
Why this answer is correct
The correct answer is D. \(x^2+6x\). The area is (x(x+6)=x-2 +6x). Exam tip: use length times breadth for rectangle area.
Step 3
Exam Tip
क्षेत्रफल (x(x+6)=x-2 +6x) है। परीक्षा में आयत का क्षेत्रफल लंबाई गुणा चौड़ाई लें।
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भुजा (s+4) वाले वर्ग का मॉडल बनाते समय \(s^2\) के अलावा कितने (4s) आयत मिलते हैं?
While making a square model of side (s+4), how many (4s) rectangles appear besides \(s^2\)?
#equal rectangles
#square model
#area
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A (2)
B (1)
C (4)
D (8)
Explanation opens after your attempt
Step 1
Concept
In ((s+4)2 ), there are two equal rectangles (4s) and (4s). Exam tip: count both rectangles using symmetry.
Step 2
Why this answer is correct
The correct answer is A. (2). In ((s+4)2 ), there are two equal rectangles (4s) and (4s). Exam tip: count both rectangles using symmetry.
Step 3
Exam Tip
((s+4)2 ) में दो समान आयत (4s) और (4s) होते हैं। परीक्षा में सममिति से दोनों आयत गिनें।
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किस क्षेत्रफल मॉडल में पूरा वर्ग \(a^2\) है और अंदर बचा वर्ग ((a-b)2 ) है?
Which area model has the whole square \(a^2\) and the inner remaining square ((a-b)2 )?
#square of difference
#visual model
#remaining square
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A योग का वर्ग मॉडल / Square of sum model
B घटाव का वर्ग मॉडल / Square of difference model
C आयत गुणन मॉडल / Rectangle multiplication model
D वर्गों के योग का मॉडल / Sum of squares model
Explanation opens after your attempt
Correct Answer
B. घटाव का वर्ग मॉडल / Square of difference model
Step 1
Concept
This visually shows ((a-b)2 ). Exam tip: observe the side (a-b) of the remaining inner square.
Step 2
Why this answer is correct
The correct answer is B. घटाव का वर्ग मॉडल / Square of difference model. This visually shows ((a-b)2 ). Exam tip: observe the side (a-b) of the remaining inner square.
Step 3
Exam Tip
यह ((a-b)2 ) को दृश्य रूप से दिखाता है। परीक्षा में शेष अंदरूनी वर्ग की भुजा (a-b) देखें।
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यदि \(x^2+2x+1\) को टाइलों से पूरा वर्ग बनाया जाए, तो भुजा क्या होगी?
If \(x^2+2x+1\) is made into a complete square using tiles, what will be the side?
#tile model
#complete square
#identity
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A (x+2)
B (2x+1)
C (x+1)
D (x-1)
Explanation opens after your attempt
Step 1
Concept
This is the tile model of ((x+1)2 ). Exam tip: treat (1) as \(1^2\).
Step 2
Why this answer is correct
The correct answer is C. (x+1). This is the tile model of ((x+1)2 ). Exam tip: treat (1) as \(1^2\).
Step 3
Exam Tip
यह ((x+1)2 ) का टाइल मॉडल है। परीक्षा में (1) को \(1^2\) समझें।
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वर्ग मॉडल में भुजा (a+b) है। बाहरी सीमा से कुल क्षेत्रफल किस रूप में सीधे मिलता है?
In a square model with side (a+b), in which form is the total area directly obtained from the outer boundary?
#outer boundary
#square area
#visual identity
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A \(a^2+2ab+b^2\)
B \(a^2-b^2\)
C (ab)
D ((a+b)2 )
Explanation opens after your attempt
Correct Answer
D. ((a+b)2 )
Step 1
Concept
The outer boundary has side (a+b), so the area is ((a+b)2 ). Exam tip: write the total area from the outside side.
Step 2
Why this answer is correct
The correct answer is D. ((a+b)2 ). The outer boundary has side (a+b), so the area is ((a+b)2 ). Exam tip: write the total area from the outside side.
Step 3
Exam Tip
बाहरी सीमा की भुजा (a+b) है इसलिए क्षेत्रफल ((a+b)2 ) है। परीक्षा में बाहर की भुजा से कुल क्षेत्रफल लिखें।
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क्षेत्रफल मॉडल में \(a^2+2ab+b^2\) और ((a+b)2 ) बराबर क्यों हैं?
Why are \(a^2+2ab+b^2\) and ((a+b)2 ) equal in an area model?
#area equality
#visual proof
#square model
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A दोनों एक ही वर्ग का क्षेत्रफल दिखाते हैं / Both show the area of the same square
B दोनों अलग अलग परिमाप दिखाते हैं / Both show different perimeters
C दोनों हमेशा शून्य होते हैं / Both are always zero
D दोनों केवल रेखाएँ दिखाते हैं / Both show only lines
Explanation opens after your attempt
Correct Answer
A. दोनों एक ही वर्ग का क्षेत्रफल दिखाते हैं / Both show the area of the same square
Step 1
Concept
One form is the sum of parts and the other is area from the outer side. Exam tip: get both forms from the same diagram.
Step 2
Why this answer is correct
The correct answer is A. दोनों एक ही वर्ग का क्षेत्रफल दिखाते हैं / Both show the area of the same square. One form is the sum of parts and the other is area from the outer side. Exam tip: get both forms from the same diagram.
Step 3
Exam Tip
एक रूप भागों का योग है और दूसरा बाहरी भुजा से क्षेत्रफल है। परीक्षा में एक ही चित्र से दोनों रूप निकालें।
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एक आयत मॉडल में ((x+2)(x-2)) दिखाया गया है। इसका सरल क्षेत्रफल क्या है?
A rectangle model shows ((x+2)(x-2)). What is its simplified area?
#sum difference
#rectangle area
#identity
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A \(x^2+4\)
B \(x^2-4\)
C \(x^2-2x\)
D \(x^2+2x\)
Explanation opens after your attempt
Correct Answer
B. \(x^2-4\)
Step 1
Concept
This is a product of sum and difference, so it gives \(x^2-4\). Exam tip: identify ((x+a)(x-a)).
Step 2
Why this answer is correct
The correct answer is B. \(x^2-4\). This is a product of sum and difference, so it gives \(x^2-4\). Exam tip: identify ((x+a)(x-a)).
Step 3
Exam Tip
यह योग और अंतर का गुणन है इसलिए \(x^2-4\) मिलता है। परीक्षा में ((x+a)(x-a)) को पहचानें।
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भुजा (2a+b) वाले वर्ग में \(b^2\) भाग किससे बनता है?
In a square of side (2a+b), how is the \(b^2\) part formed?
#small square
#b square
#area model
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A (2a) और (b) के आयत से / From a rectangle of (2a) and (b)
B (2a) के वर्ग से / From the square of (2a)
C (b) के वर्ग से / From the square of (b)
D (a) और (b) के योग से / From the sum of (a) and (b)
Explanation opens after your attempt
Correct Answer
C. (b) के वर्ग से / From the square of (b)
Step 1
Concept
\(b^2\) is the area of the small square with side (b). Exam tip: connect a square term with the square of its side.
Step 2
Why this answer is correct
The correct answer is C. (b) के वर्ग से / From the square of (b). \(b^2\) is the area of the small square with side (b). Exam tip: connect a square term with the square of its side.
Step 3
Exam Tip
\(b^2\) भुजा (b) वाले छोटे वर्ग का क्षेत्रफल है। परीक्षा में वर्ग पद को उसी भुजा के वर्ग से जोड़ें।
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यदि आयत की भुजाएँ (a+b) और (c) हैं, तो क्षेत्रफल मॉडल में दो भाग कौन से होंगे?
If the sides of a rectangle are (a+b) and (c), what two parts appear in the area model?
#distributive area
#rectangle model
#visual algebra
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A (ac) और (bc) / (ac) and (bc)
B (ab) और \(c^2\) / (ab) and \(c^2\)
C \(a^2\) और \(b^2\) / \(a^2\) and \(b^2\)
D (a+b) और (c) / (a+b) and (c)
Explanation opens after your attempt
Correct Answer
A. (ac) और (bc) / (ac) and (bc)
Step 1
Concept
(c(a+b)=ac+bc). Exam tip: split one side into two parts and add areas.
Step 2
Why this answer is correct
The correct answer is A. (ac) और (bc) / (ac) and (bc). (c(a+b)=ac+bc). Exam tip: split one side into two parts and add areas.
Step 3
Exam Tip
(c(a+b)=ac+bc) होता है। परीक्षा में एक भुजा को दो भागों में बाँटकर क्षेत्रफल जोड़ें।
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वर्ग मॉडल में \(x^2-6x+9\) दिखता है। यह किस भुजा वाले वर्ग का क्षेत्रफल है?
A square model shows \(x^2-6x+9\). It is the area of a square with which side?
#square difference
#perfect square
#visual model
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A (x+3)
B (x-3)
C (x-6)
D (x+9)
Explanation opens after your attempt
Step 1
Concept
Since \(9=3^2\) and the middle term is (-6x), the side is (x-3). Exam tip: identify subtraction from the negative middle term.
Step 2
Why this answer is correct
The correct answer is B. (x-3). Since \(9=3^2\) and the middle term is (-6x), the side is (x-3). Exam tip: identify subtraction from the negative middle term.
Step 3
Exam Tip
\(9=3^2\) और बीच का पद (-6x) है इसलिए भुजा (x-3) है। परीक्षा में ऋणात्मक बीच पद से घटाव पहचानें।
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टाइल मॉडल में \(x^2\) टाइल और (1) टाइल के बीच दो (x) टाइलें लगाकर कौन सा पूर्ण वर्ग बनता है?
In a tile model, placing two (x) tiles between an \(x^2\) tile and a unit tile forms which perfect square?
#algebra tiles
#complete square
#visual identity
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A ((x+2)2 )
B \(x^2+1\)
C ((x+1)2 )
D \(x^2+2\)
Explanation opens after your attempt
Correct Answer
C. ((x+1)2 )
Step 1
Concept
The total tiles give \(x^2+2x+1\). Exam tip: two (x) tiles form ((x+1)2 ).
Step 2
Why this answer is correct
The correct answer is C. ((x+1)2 ). The total tiles give \(x^2+2x+1\). Exam tip: two (x) tiles form ((x+1)2 ).
Step 3
Exam Tip
कुल टाइलें \(x^2+2x+1\) देती हैं। परीक्षा में दो (x) टाइलें ((x+1)2 ) बनाती हैं।
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यदि बड़े वर्ग की भुजा (10) और छोटे वर्ग की भुजा (4) है, तो वर्गों के अंतर का क्षेत्रफल क्या होगा?
If the side of the big square is (10) and the side of the small square is (4), what is the area of the difference of squares?
#numeric visual model
#difference of squares
#area
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A (40)
B (60)
C (84)
D (116)
Explanation opens after your attempt
Step 1
Concept
The area is \(10^2-4^2=100-16=84\). Exam tip: square first, then subtract.
Step 2
Why this answer is correct
The correct answer is C. (84). The area is \(10^2-4^2=100-16=84\). Exam tip: square first, then subtract.
Step 3
Exam Tip
क्षेत्रफल \(10^2-4^2=100-16=84\) है। परीक्षा में पहले वर्ग करें फिर घटाएँ।
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एक वर्ग मॉडल में बाहरी भुजा (x+8) है। क्षेत्रफल के विस्तार में अंतिम पद क्या होगा?
In a square model, the outer side is (x+8). What will be the last term in the expansion of the area?
#last term
#square model
#binomial
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A (8x)
B (16x)
C \(x^2\)
D (64)
Explanation opens after your attempt
Step 1
Concept
The last term is \(8^2=64\). Exam tip: the square of the constant part becomes the last term.
Step 2
Why this answer is correct
The correct answer is D. (64). The last term is \(8^2=64\). Exam tip: the square of the constant part becomes the last term.
Step 3
Exam Tip
अंतिम पद \(8^2=64\) है। परीक्षा में स्थिर भाग का वर्ग अंतिम पद होता है।
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दृश्य मॉडल में ((a+b)2 ) का (2ab) भाग किससे आता है?
In the visual model of ((a+b)2 ), where does the (2ab) part come from?
#middle term
#ab rectangles
#visual proof
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A दो (ab) आयतों से / From two (ab) rectangles
B एक \(a^2\) वर्ग से / From one \(a^2\) square
C एक \(b^2\) वर्ग से / From one \(b^2\) square
D बाहरी परिमाप से / From the outer perimeter
Explanation opens after your attempt
Correct Answer
A. दो (ab) आयतों से / From two (ab) rectangles
Step 1
Concept
Two equal rectangles of areas (ab) and (ab) combine to form (2ab). Exam tip: connect the middle term with rectangles.
Step 2
Why this answer is correct
The correct answer is A. दो (ab) आयतों से / From two (ab) rectangles. Two equal rectangles of areas (ab) and (ab) combine to form (2ab). Exam tip: connect the middle term with rectangles.
Step 3
Exam Tip
दो समान आयतों के क्षेत्रफल (ab) और (ab) मिलकर (2ab) बनाते हैं। परीक्षा में बीच पद को आयतों से जोड़ें।
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भुजाएँ (x+3) और (x-3) वाले आयत का मॉडल कौन सी पहचान दिखाता है?
A rectangle with sides (x+3) and (x-3) shows which identity?
#rectangle identity
#sum difference
#visual model
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A ((x+3)2 =x-2 +6x+9)
B ((x+3)(x-3)=x-2 -9)
C ((x-3)2 =x-2 -6x+9)
D (x-2 +9=(x+3)(x-3))
Explanation opens after your attempt
Correct Answer
B. ((x+3)(x-3)=x-2 -9)
Step 1
Concept
This is a sum-and-difference rectangle, so the area is \(x^2-9\). Exam tip: notice the same number (3) to identify difference of squares.
Step 2
Why this answer is correct
The correct answer is B. ((x+3)(x-3)=x-2 -9). This is a sum-and-difference rectangle, so the area is \(x^2-9\). Exam tip: notice the same number (3) to identify difference of squares.
Step 3
Exam Tip
यह योग और अंतर का आयत है इसलिए क्षेत्रफल \(x^2-9\) है। परीक्षा में समान संख्या (3) देखकर वर्गों का अंतर पहचानें।
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