भुजा \(a+b\) वाले वर्ग का क्षेत्र मॉडल किस बीजीय पहचान को दिखाता है?
Which algebraic identity is shown by the area model of a square with side \(a+b\)?
#algebraic identities
#area model
#square
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A \( (a+b)^2=a^2+2ab+b^2 \)
B \( (a-b)^2=a^2-2ab+b^2 \)
C \( a^2-b^2=(a+b)(a-b) \)
D \( a+b=ab \)
Explanation opens after your attempt
Correct Answer
A. \( (a+b)^2=a^2+2ab+b^2 \)
Step 1
Concept
Splitting the square into two smaller squares and two rectangles gives \(a^2+2ab+b^2\). Exam tip: connect square area with the identity.
Step 2
Why this answer is correct
The correct answer is A. \( (a+b)^2=a^2+2ab+b^2 \). Splitting the square into two smaller squares and two rectangles gives \(a^2+2ab+b^2\). Exam tip: connect square area with the identity.
Step 3
Exam Tip
वर्ग को दो छोटे वर्गों और दो आयतों में बांटने पर कुल क्षेत्र \(a^2+2ab+b^2\) मिलता है। परीक्षा में वर्ग का क्षेत्र पहचान से जोड़ें।
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भुजा \(x+3\) वाले वर्ग को देखकर \((x+3)^2\) का विस्तार क्या होगा?
By observing a square of side \(x+3\), what is the expansion of \((x+3)^2\)?
#visual model
#identity expansion
#class 9 math
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A \(x^2+3x+9\)
B \(x^2+6x+9\)
C \(x^2-6x+9\)
D \(x^2+9x+6\)
Explanation opens after your attempt
Correct Answer
B. \(x^2+6x+9\)
Step 1
Concept
The area model has \(x^2\), two \(3x\) rectangles, and \(9\). Exam tip: the middle term comes from two equal rectangles.
Step 2
Why this answer is correct
The correct answer is B. \(x^2+6x+9\). The area model has \(x^2\), two \(3x\) rectangles, and \(9\). Exam tip: the middle term comes from two equal rectangles.
Step 3
Exam Tip
क्षेत्र मॉडल में \(x^2\), दो \(3x\) आयत और \(9\) वर्ग मिलते हैं। परीक्षा में बीच का पद दो समान आयतों से आता है।
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एक बड़े वर्ग की भुजा \(a\) है और उसमें से भुजा \(b\) का वर्ग हटाया गया है। बचा क्षेत्र किससे व्यक्त होगा?
A large square has side \(a\), and a square of side \(b\) is removed from it. How is the remaining area expressed?
#difference of squares
#area model
#visual identity
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A \(a^2+b^2\)
B \(2ab\)
C \(a^2-b^2\)
D \(a-b\)
Explanation opens after your attempt
Correct Answer
C. \(a^2-b^2\)
Step 1
Concept
The smaller area \(b^2\) is subtracted from the larger area \(a^2\). Exam tip: treat the removed part as subtraction.
Step 2
Why this answer is correct
The correct answer is C. \(a^2-b^2\). The smaller area \(b^2\) is subtracted from the larger area \(a^2\). Exam tip: treat the removed part as subtraction.
Step 3
Exam Tip
बड़े वर्ग के क्षेत्र \(a^2\) में से छोटे वर्ग का क्षेत्र \(b^2\) घटता है। परीक्षा में हटाए गए भाग को घटाव मानें।
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आयाम \(a+b\) और \(a-b\) वाले आयत का क्षेत्र किस पहचान से जुड़ा है?
The area of a rectangle with dimensions \(a+b\) and \(a-b\) is linked with which identity?
#rectangle model
#difference identity
#algebra
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A \(a^2+2ab+b^2\)
B \(a^2-2ab+b^2\)
C \(2a+2b\)
D \(a^2-b^2\)
Explanation opens after your attempt
Correct Answer
D. \(a^2-b^2\)
Step 1
Concept
The rectangle area is \((a+b)(a-b)\), which equals \(a^2-b^2\). Exam tip: multiply length and breadth.
Step 2
Why this answer is correct
The correct answer is D. \(a^2-b^2\). The rectangle area is \((a+b)(a-b)\), which equals \(a^2-b^2\). Exam tip: multiply length and breadth.
Step 3
Exam Tip
आयत का क्षेत्र \((a+b)(a-b)\) होता है जो \(a^2-b^2\) के बराबर है। परीक्षा में लंबाई और चौड़ाई को गुणा करें।
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भुजा \(x-2\) वाले वर्ग का क्षेत्र मॉडल किस विस्तार को सही दिखाता है?
Which expansion is correctly shown by the area model of a square with side \(x-2\)?
#square model
#minus identity
#easy algebra
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A \(x^2-4x+4\)
B \(x^2+4x+4\)
C \(x^2-2x+4\)
D \(x^2+2x-4\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-4x+4\)
Step 1
Concept
In \((x-2)^2\), there is \(x^2\), two subtracted \(2x\) parts, and \(4\) added. Exam tip: watch the negative sign.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-4x+4\). In \((x-2)^2\), there is \(x^2\), two subtracted \(2x\) parts, and \(4\) added. Exam tip: watch the negative sign.
Step 3
Exam Tip
\((x-2)^2\) में \(x^2\), घटे हुए दो \(2x\) भाग और \(4\) जुड़ता है। परीक्षा में ऋण चिह्न का ध्यान रखें।
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यदि वर्ग को \(p^2\), \(pq\), \(pq\) और \(q^2\) भागों में बांटा गया है, तो कुल क्षेत्र क्या है?
If a square is divided into parts \(p^2\), \(pq\), \(pq\), and \(q^2\), what is its total area?
#area partition
#square identity
#visual algebra
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A \(p^2+q^2\)
B \(p^2+2pq+q^2\)
C \(p^2-2pq+q^2\)
D \(2p+2q\)
Explanation opens after your attempt
Correct Answer
B. \(p^2+2pq+q^2\)
Step 1
Concept
The two \(pq\) rectangles combine to make \(2pq\). Exam tip: do not forget to add equal rectangles.
Step 2
Why this answer is correct
The correct answer is B. \(p^2+2pq+q^2\). The two \(pq\) rectangles combine to make \(2pq\). Exam tip: do not forget to add equal rectangles.
Step 3
Exam Tip
दोनों \(pq\) आयत मिलकर \(2pq\) बनाते हैं। परीक्षा में समान आयतों को जोड़ना न भूलें।
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भुजा \(m+n\) वाले वर्ग के चार भागों में सबसे बड़ा वर्गीय भाग कौन सा हो सकता है?
In a square of side \(m+n\), which can be the largest square part among its four parts?
#visual parts
#square identity
#area tiles
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A \(mn\)
B \(2mn\)
C \(m^2\)
D \(m+n\)
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Correct Answer
C. \(m^2\)
Step 1
Concept
The square parts are \(m^2\) and \(n^2\), and if \(m>n\), then \(m^2\) is larger. Exam tip: distinguish square and rectangular parts.
Step 2
Why this answer is correct
The correct answer is C. \(m^2\). The square parts are \(m^2\) and \(n^2\), and if \(m>n\), then \(m^2\) is larger. Exam tip: distinguish square and rectangular parts.
Step 3
Exam Tip
वर्गीय भागों में \(m^2\) और \(n^2\) आते हैं और \(m>n\) हो तो \(m^2\) बड़ा होगा। परीक्षा में वर्गीय और आयताकार भाग अलग पहचानें।
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एक \(x\) बाय \(x\) वर्ग और दो \(x\) बाय \(5\) आयतों के साथ \(5\) बाय \(5\) वर्ग जोड़ा गया है। यह किसका मॉडल है?
An \(x\) by \(x\) square, two \(x\) by \(5\) rectangles, and one \(5\) by \(5\) square are combined. This is a model of what?
#algebra tiles
#square expansion
#visual model
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A \((x-5)^2\)
B \(x^2-25\)
C \(x^2+5x+25\)
D \((x+5)^2\)
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Correct Answer
D. \((x+5)^2\)
Step 1
Concept
The total area is \(x^2+10x+25\). Exam tip: write two \(5x\) rectangles as \(10x\).
Step 2
Why this answer is correct
The correct answer is D. \((x+5)^2\). The total area is \(x^2+10x+25\). Exam tip: write two \(5x\) rectangles as \(10x\).
Step 3
Exam Tip
दिए गए भागों का कुल क्षेत्र \(x^2+10x+25\) है। परीक्षा में दो \(5x\) आयतों को \(10x\) लिखें।
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यदि दृश्य मॉडल में \(y^2\) वर्ग से दो \(4y\) आयत घटाए जाते हैं और \(16\) वर्ग जोड़ा जाता है, तो पहचान क्या है?
If a visual model subtracts two \(4y\) rectangles from a \(y^2\) square and adds a \(16\) square, what is the identity?
#minus square
#visual identity
#algebraic model
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A \((y-4)^2=y^2-8y+16\)
B \((y+4)^2=y^2+8y+16\)
C \(y^2-16=(y-4)(y+4)\)
D \(y^2+4y+16\)
Explanation opens after your attempt
Correct Answer
A. \((y-4)^2=y^2-8y+16\)
Step 1
Concept
Subtracting two \(4y\) parts gives the middle term \(-8y\). Exam tip: remember \(4^2=16\).
Step 2
Why this answer is correct
The correct answer is A. \((y-4)^2=y^2-8y+16\). Subtracting two \(4y\) parts gives the middle term \(-8y\). Exam tip: remember \(4^2=16\).
Step 3
Exam Tip
दो \(4y\) घटने से बीच का पद \(-8y\) बनता है। परीक्षा में \(4^2=16\) याद रखें।
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भुजा \(6+2\) वाले वर्ग के क्षेत्र मॉडल में कुल क्षेत्र किस रूप में लिखा जा सकता है?
In the area model of a square with side \(6+2\), how can the total area be written?
#numeric area model
#square identity
#easy
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A \(36+4\)
B \(36+24+4\)
C \(12+8\)
D \(64-4\)
Explanation opens after your attempt
Correct Answer
B. \(36+24+4\)
Step 1
Concept
In \((6+2)^2\), \(6^2\), two \(6\times2\) parts, and \(2^2\) are added. Exam tip: understand the identity using numerical models.
Step 2
Why this answer is correct
The correct answer is B. \(36+24+4\). In \((6+2)^2\), \(6^2\), two \(6\times2\) parts, and \(2^2\) are added. Exam tip: understand the identity using numerical models.
Step 3
Exam Tip
\((6+2)^2\) में \(6^2\), दो \(6\times2\) और \(2^2\) जुड़ते हैं। परीक्षा में संख्यात्मक मॉडल से पहचान समझें।
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किस दृश्य मॉडल में बीच के दो आयतों का क्षेत्र बराबर \(ab\) और \(ab\) होता है?
In which visual model are the two middle rectangles equal to \(ab\) and \(ab\)?
#middle term
#area model
#identity
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A \((a-b)(a+b)\)
B \(a^2-b^2\)
C \((a+b)^2\)
D \(a+b\)
Explanation opens after your attempt
Correct Answer
C. \((a+b)^2\)
Step 1
Concept
In the square model of \((a+b)^2\), two equal rectangles are \(ab\). Exam tip: write the total middle area as \(2ab\).
Step 2
Why this answer is correct
The correct answer is C. \((a+b)^2\). In the square model of \((a+b)^2\), two equal rectangles are \(ab\). Exam tip: write the total middle area as \(2ab\).
Step 3
Exam Tip
\((a+b)^2\) के वर्ग मॉडल में दो बराबर आयत \(ab\) के होते हैं। परीक्षा में बीच का कुल क्षेत्र \(2ab\) लिखें।
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एक आयत की लंबाई \(r+s\) और चौड़ाई \(r\) है। क्षेत्र मॉडल में कुल क्षेत्र क्या होगा?
A rectangle has length \(r+s\) and breadth \(r\). What will be the total area in the area model?
#rectangle area
#distributive model
#visual algebra
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A \(r^2+rs\)
B \(r^2+s^2\)
C \(2rs\)
D \(r+s\)
Explanation opens after your attempt
Correct Answer
A. \(r^2+rs\)
Step 1
Concept
Splitting the length into \(r\) and \(s\) gives area \(r^2+rs\). Exam tip: connect distributive law with area.
Step 2
Why this answer is correct
The correct answer is A. \(r^2+rs\). Splitting the length into \(r\) and \(s\) gives area \(r^2+rs\). Exam tip: connect distributive law with area.
Step 3
Exam Tip
लंबाई को \(r\) और \(s\) में बांटने पर क्षेत्र \(r^2+rs\) मिलता है। परीक्षा में वितरण नियम को क्षेत्र से जोड़ें।
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अलजेब्रा टाइल में \(x^2\) टाइल, \(7x\) टाइल और \(12\) इकाई टाइलें मिलकर कौन सा क्षेत्र दिखा सकती हैं?
In algebra tiles, \(x^2\) tile, \(7x\) tiles, and \(12\) unit tiles can show which area?
#algebra tiles
#area expression
#visual model
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A \(x^2+12x+7\)
B \(x^2+7x+12\)
C \(x^2-7x+12\)
D \(7x^2+12\)
Explanation opens after your attempt
Correct Answer
B. \(x^2+7x+12\)
Step 1
Concept
The tile areas add directly to make \(x^2+7x+12\). Exam tip: count like tiles.
Step 2
Why this answer is correct
The correct answer is B. \(x^2+7x+12\). The tile areas add directly to make \(x^2+7x+12\). Exam tip: count like tiles.
Step 3
Exam Tip
टाइलों के क्षेत्र सीधे जुड़कर \(x^2+7x+12\) बनाते हैं। परीक्षा में समान टाइलों की संख्या गिनें।
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यदि \((x+2)(x+3)\) को आयत से दिखाया जाए, तो चार भागों का योग क्या होगा?
If \((x+2)(x+3)\) is shown by a rectangle, what is the sum of its four parts?
#rectangle expansion
#visual multiplication
#identity
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A \(x^2+5\)
B \(x^2+6x+5\)
C \(x^2+5x+6\)
D \(x^2+2x+3\)
Explanation opens after your attempt
Correct Answer
C. \(x^2+5x+6\)
Step 1
Concept
The parts are \(x^2\), \(3x\), \(2x\), and \(6\). Exam tip: add \(3x+2x=5x\).
Step 2
Why this answer is correct
The correct answer is C. \(x^2+5x+6\). The parts are \(x^2\), \(3x\), \(2x\), and \(6\). Exam tip: add \(3x+2x=5x\).
Step 3
Exam Tip
भाग \(x^2\), \(3x\), \(2x\) और \(6\) हैं। परीक्षा में \(3x+2x=5x\) जोड़ें।
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भुजा \(t+1\) वाले वर्ग का क्षेत्र मॉडल किस परिणाम तक पहुंचाता है?
The area model of a square with side \(t+1\) leads to which result?
#square of binomial
#visual model
#identity
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A \(t^2+1\)
B \(t^2-t+1\)
C \(t^2+3t+1\)
D \(t^2+2t+1\)
Explanation opens after your attempt
Correct Answer
D. \(t^2+2t+1\)
Step 1
Concept
Because of two \(t\) rectangles, the middle term is \(2t\). Exam tip: also add \(1^2=1\).
Step 2
Why this answer is correct
The correct answer is D. \(t^2+2t+1\). Because of two \(t\) rectangles, the middle term is \(2t\). Exam tip: also add \(1^2=1\).
Step 3
Exam Tip
दो \(t\) आयतों के कारण बीच का पद \(2t\) बनता है। परीक्षा में \(1^2=1\) भी जोड़ें।
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किस मॉडल में \(a^2\) वर्ग के एक कोने से \(b^2\) वर्ग हटाकर शेष को आयत में बदला जा सकता है?
In which model can a \(b^2\) square be removed from a corner of an \(a^2\) square and the remaining part rearranged into a rectangle?
#difference of squares
#rearrangement
#visual proof
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A \(a^2-b^2=(a+b)(a-b)\)
B \(a^2+b^2=(a+b)^2\)
C \(a^2+2ab+b^2=(a-b)^2\)
D \(ab=a+b\)
Explanation opens after your attempt
Correct Answer
A. \(a^2-b^2=(a+b)(a-b)\)
Step 1
Concept
This is the visual explanation of difference of squares. Exam tip: remember the rearrangement as \((a+b)(a-b)\).
Step 2
Why this answer is correct
The correct answer is A. \(a^2-b^2=(a+b)(a-b)\). This is the visual explanation of difference of squares. Exam tip: remember the rearrangement as \((a+b)(a-b)\).
Step 3
Exam Tip
यह अंतर के वर्गों की दृश्य व्याख्या है। परीक्षा में पुनर्व्यवस्था से \((a+b)(a-b)\) याद रखें।
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भुजा \(10-3\) वाले वर्ग के क्षेत्र मॉडल में सही विस्तार कौन सा है?
Which is the correct expansion in the area model of a square with side \(10-3\)?
#numeric square
#minus model
#identity
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A \(100-9\)
B \(100-60+9\)
C \(100+60+9\)
D \(100-30+9\)
Explanation opens after your attempt
Correct Answer
B. \(100-60+9\)
Step 1
Concept
\((10-3)^2\) equals \(10^2-2\times10\times3+3^2\). Exam tip: do not forget the subtraction of \(2ab\).
Step 2
Why this answer is correct
The correct answer is B. \(100-60+9\). \((10-3)^2\) equals \(10^2-2\times10\times3+3^2\). Exam tip: do not forget the subtraction of \(2ab\).
Step 3
Exam Tip
\((10-3)^2\) में \(10^2-2\times10\times3+3^2\) होता है। परीक्षा में \(2ab\) वाला घटाव न भूलें।
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एक वर्ग की भुजा \(a+b+c\) है। दृश्य मॉडल में कुल क्षेत्र को कितने मुख्य प्रकार के पदों में सोचा जा सकता है?
A square has side \(a+b+c\). In the visual model, the total area can be thought of in how many main types of terms?
#three terms
#visual area
#algebraic identity
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A केवल वर्ग पद / Only square terms
B केवल आयत पद / Only rectangle terms
C वर्ग पद और आयत पद / Square terms and rectangle terms
D केवल रेखा पद / Only line terms
Explanation opens after your attempt
Correct Answer
C. वर्ग पद और आयत पद / Square terms and rectangle terms
Step 1
Concept
Such a model has squares like \(a^2\), \(b^2\), \(c^2\) and rectangles like \(ab\), \(bc\), \(ca\). Exam tip: identify area terms by shape.
Step 2
Why this answer is correct
The correct answer is C. वर्ग पद और आयत पद / Square terms and rectangle terms. Such a model has squares like \(a^2\), \(b^2\), \(c^2\) and rectangles like \(ab\), \(bc\), \(ca\). Exam tip: identify area terms by shape.
Step 3
Exam Tip
ऐसे मॉडल में \(a^2\), \(b^2\), \(c^2\) जैसे वर्ग और \(ab\), \(bc\), \(ca\) जैसे आयत आते हैं। परीक्षा में क्षेत्र पदों को आकार से पहचानें।
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यदि किसी आयत को \(x^2\), \(4x\), \(2x\) और \(8\) भागों में बांटा गया है, तो आयाम क्या हो सकते हैं?
If a rectangle is divided into parts \(x^2\), \(4x\), \(2x\), and \(8\), what can its dimensions be?
#area rectangle
#factor model
#visual algebra
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A \(x+8\) और \(x+1\) / \(x+8\) and \(x+1\)
B \(x+4\) और \(x+2\) / \(x+4\) and \(x+2\)
C \(x-4\) और \(x-2\) / \(x-4\) and \(x-2\)
D \(x+6\) और \(x+8\) / \(x+6\) and \(x+8\)
Explanation opens after your attempt
Correct Answer
B. \(x+4\) और \(x+2\) / \(x+4\) and \(x+2\)
Step 1
Concept
With \(4x\) and \(2x\), the corner \(8\) shows the numbers are \(4\) and \(2\). Exam tip: look at the product in the corner.
Step 2
Why this answer is correct
The correct answer is B. \(x+4\) और \(x+2\) / \(x+4\) and \(x+2\). With \(4x\) and \(2x\), the corner \(8\) shows the numbers are \(4\) and \(2\). Exam tip: look at the product in the corner.
Step 3
Exam Tip
\(4x\) और \(2x\) के साथ कोना \(8\) बताता है कि संख्याएं \(4\) और \(2\) हैं। परीक्षा में कोने के गुणनफल को देखें।
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दृश्य मॉडल में \(a^2+2ab+b^2\) को एक पूर्ण वर्ग के रूप में क्यों दिखाया जाता है?
Why is \(a^2+2ab+b^2\) shown as a complete square in a visual model?
#perfect square trinomial
#visual model
#identity
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A क्योंकि इसके भाग मिलकर भुजा \(a+b\) का वर्ग बनाते हैं / Because its parts form a square of side \(a+b\)
B क्योंकि इसमें केवल एक आयत होता है / Because it has only one rectangle
C क्योंकि इसका क्षेत्र हमेशा \(ab\) होता है / Because its area is always \(ab\)
D क्योंकि \(a\) और \(b\) शून्य होते हैं / Because \(a\) and \(b\) are zero
Explanation opens after your attempt
Correct Answer
A. क्योंकि इसके भाग मिलकर भुजा \(a+b\) का वर्ग बनाते हैं / Because its parts form a square of side \(a+b\)
Step 1
Concept
Two squares and two rectangles form one complete square. Exam tip: identify a perfect square trinomial from the figure.
Step 2
Why this answer is correct
The correct answer is A. क्योंकि इसके भाग मिलकर भुजा \(a+b\) का वर्ग बनाते हैं / Because its parts form a square of side \(a+b\). Two squares and two rectangles form one complete square. Exam tip: identify a perfect square trinomial from the figure.
Step 3
Exam Tip
दो वर्ग और दो आयत मिलकर पूरा वर्ग बनाते हैं। परीक्षा में पूर्ण वर्ग त्रिपद को चित्र से पहचानें।
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किस आकृति का क्षेत्र \((p+q)^2\) को सबसे सीधे दिखाता है?
Which figure most directly shows the area \((p+q)^2\)?
#square area
#visual representation
#identity
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A लंबाई \(p+q\) और चौड़ाई \(p-q\) वाला आयत / Rectangle with length \(p+q\) and breadth \(p-q\)
B भुजा \(p+q\) वाला वर्ग / Square with side \(p+q\)
C भुजा \(p-q\) वाला वर्ग / Square with side \(p-q\)
D लंबाई \(p\) और चौड़ाई \(q\) वाला आयत / Rectangle with length \(p\) and breadth \(q\)
Explanation opens after your attempt
Correct Answer
B. भुजा \(p+q\) वाला वर्ग / Square with side \(p+q\)
Step 1
Concept
The area of a square equals the square of its side. Exam tip: think of a square for \((p+q)^2\).
Step 2
Why this answer is correct
The correct answer is B. भुजा \(p+q\) वाला वर्ग / Square with side \(p+q\). The area of a square equals the square of its side. Exam tip: think of a square for \((p+q)^2\).
Step 3
Exam Tip
वर्ग का क्षेत्र भुजा के वर्ग के बराबर होता है। परीक्षा में \((p+q)^2\) के लिए वर्ग सोचें।
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एक चित्र में \(a^2\) और \(b^2\) वर्गों के साथ दो \(ab\) आयत जोड़े गए हैं। कुल क्षेत्र क्या होगा?
In a diagram, two \(ab\) rectangles are added with \(a^2\) and \(b^2\) squares. What will be the total area?
#area addition
#binomial square
#visual identity
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A \(a^2+b^2\)
B \(a^2-ab+b^2\)
C \(a^2+2ab+b^2\)
D \(a^2-2ab+b^2\)
Explanation opens after your attempt
Correct Answer
C. \(a^2+2ab+b^2\)
Step 1
Concept
The sum of two \(ab\) rectangles is \(2ab\). Exam tip: add the area of every part.
Step 2
Why this answer is correct
The correct answer is C. \(a^2+2ab+b^2\). The sum of two \(ab\) rectangles is \(2ab\). Exam tip: add the area of every part.
Step 3
Exam Tip
दो \(ab\) आयतों का योग \(2ab\) है। परीक्षा में हर भाग का क्षेत्र जोड़ें।
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भुजा \(z-1\) वाले वर्ग के मॉडल में कौन सा पद धनात्मक रहता है?
In the model of a square with side \(z-1\), which term remains positive?
#minus square
#signs
#visual model
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A \(-2z\)
B \(-z^2\)
C \(-1\)
D \(1\)
Explanation opens after your attempt
Step 1
Concept
In \((z-1)^2=z^2-2z+1\), the last square term \(1\) is positive. Exam tip: keep the squared term positive.
Step 2
Why this answer is correct
The correct answer is D. \(1\). In \((z-1)^2=z^2-2z+1\), the last square term \(1\) is positive. Exam tip: keep the squared term positive.
Step 3
Exam Tip
\((z-1)^2=z^2-2z+1\) में अंतिम वर्ग पद \(1\) धनात्मक है। परीक्षा में वर्ग किए गए पद का चिह्न धनात्मक रखें।
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यदि \(a\) बाय \(a\) वर्ग के साथ \(a\) बाय \(b\) आयत जोड़ा जाए, तो बना क्षेत्र किस रूप में लिखा जा सकता है?
If an \(a\) by \(a\) square is joined with an \(a\) by \(b\) rectangle, how can the formed area be written?
#common factor
#area model
#visual algebra
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A \(a(a+b)\)
B \(a+b\)
C \(a^2+b^2\)
D \(ab^2\)
Explanation opens after your attempt
Correct Answer
A. \(a(a+b)\)
Step 1
Concept
The total area is \(a^2+ab\), which can be written as \(a(a+b)\). Exam tip: identify the common factor from the diagram.
Step 2
Why this answer is correct
The correct answer is A. \(a(a+b)\). The total area is \(a^2+ab\), which can be written as \(a(a+b)\). Exam tip: identify the common factor from the diagram.
Step 3
Exam Tip
कुल क्षेत्र \(a^2+ab\) है जिसे \(a(a+b)\) लिखा जा सकता है। परीक्षा में सामान्य गुणनखंड को चित्र से पहचानें।
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एक आयत के भाग \(x^2\), \(5x\), \(x\) और \(5\) हैं। यह किस गुणन को दिखाता है?
A rectangle has parts \(x^2\), \(5x\), \(x\), and \(5\). Which multiplication does it show?
#rectangle multiplication
#algebra tiles
#factors
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A \((x+5)(x+5)\)
B \((x+5)(x+1)\)
C \((x-5)(x-1)\)
D \((x+6)(x+5)\)
Explanation opens after your attempt
Correct Answer
B. \((x+5)(x+1)\)
Step 1
Concept
The sum of parts is \(x^2+6x+5\), which matches \((x+5)(x+1)\). Exam tip: read the outside dimensions.
Step 2
Why this answer is correct
The correct answer is B. \((x+5)(x+1)\). The sum of parts is \(x^2+6x+5\), which matches \((x+5)(x+1)\). Exam tip: read the outside dimensions.
Step 3
Exam Tip
भागों का योग \(x^2+6x+5\) है जो \((x+5)(x+1)\) से मिलता है। परीक्षा में बाहरी आयाम पढ़ें।
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किस दृश्य प्रमाण में एक ही क्षेत्र को दो तरीकों से लिखकर पहचान सिद्ध की जाती है?
In which visual proof is an identity proved by writing the same area in two ways?
#visual proof
#area model
#identity
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A क्षेत्र मॉडल / Area model
B संख्या रेखा मॉडल / Number line model
C घड़ी मॉडल / Clock model
D तालिका मॉडल / Table model
Explanation opens after your attempt
Correct Answer
A. क्षेत्र मॉडल / Area model
Step 1
Concept
In an area model, the same figure's area is written in different forms. Exam tip: keep both forms equal.
Step 2
Why this answer is correct
The correct answer is A. क्षेत्र मॉडल / Area model. In an area model, the same figure's area is written in different forms. Exam tip: keep both forms equal.
Step 3
Exam Tip
क्षेत्र मॉडल में एक ही आकृति का क्षेत्र अलग रूपों में लिखा जाता है। परीक्षा में दोनों रूपों को बराबर रखें।
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भुजा \(x+y\) वाले वर्ग में \(x^2\) और \(y^2\) के अलावा कौन से भाग मिलते हैं?
In a square of side \(x+y\), apart from \(x^2\) and \(y^2\), which parts are obtained?
#square partition
#middle rectangles
#visual identity
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A दो \(xy\) आयत / Two \(xy\) rectangles
B एक \(x+y\) रेखा / One \(x+y\) line
C दो \(x^2\) वर्ग / Two \(x^2\) squares
D एक \(x-y\) आयत / One \(x-y\) rectangle
Explanation opens after your attempt
Correct Answer
A. दो \(xy\) आयत / Two \(xy\) rectangles
Step 1
Concept
The square model has two equal rectangles made from \(x\) and \(y\). Exam tip: convert them into \(2xy\).
Step 2
Why this answer is correct
The correct answer is A. दो \(xy\) आयत / Two \(xy\) rectangles. The square model has two equal rectangles made from \(x\) and \(y\). Exam tip: convert them into \(2xy\).
Step 3
Exam Tip
वर्ग मॉडल में \(x\) और \(y\) से बने दो बराबर आयत आते हैं। परीक्षा में इन्हें \(2xy\) में बदलें।
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यदि आयत की लंबाई \(x+4\) और चौड़ाई \(x+4\) है, तो यह किस आकृति के बराबर है?
If a rectangle has length \(x+4\) and breadth \(x+4\), which figure is it equivalent to?
#square recognition
#area model
#identity
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A लंबाई \(x\) और चौड़ाई \(4\) वाला आयत / Rectangle with length \(x\) and breadth \(4\)
B भुजा \(x+4\) वाला वर्ग / Square with side \(x+4\)
C भुजा \(x-4\) वाला वर्ग / Square with side \(x-4\)
D लंबाई \(x+8\) और चौड़ाई \(x\) वाला आयत / Rectangle with length \(x+8\) and breadth \(x\)
Explanation opens after your attempt
Correct Answer
B. भुजा \(x+4\) वाला वर्ग / Square with side \(x+4\)
Step 1
Concept
When both dimensions are equal, the figure is a square. Exam tip: treat equal length and breadth as a square.
Step 2
Why this answer is correct
The correct answer is B. भुजा \(x+4\) वाला वर्ग / Square with side \(x+4\). When both dimensions are equal, the figure is a square. Exam tip: treat equal length and breadth as a square.
Step 3
Exam Tip
दोनों आयाम बराबर हों तो आकृति वर्ग होती है। परीक्षा में बराबर लंबाई और चौड़ाई को वर्ग मानें।
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दृश्य मॉडल में \((a-b)^2\) के लिए \(a^2\) से कौन सा कुल आयताकार क्षेत्र घटता है?
In the visual model of \((a-b)^2\), what total rectangular area is subtracted from \(a^2\)?
#subtraction model
#minus square
#area identity
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A \(ab\)
B \(b^2\)
C \(2ab\)
D \(a^2\)
Explanation opens after your attempt
Correct Answer
C. \(2ab\)
Step 1
Concept
Two \(ab\) strips are removed, so the total subtraction is \(2ab\). Exam tip: \(b^2\) is added back later.
Step 2
Why this answer is correct
The correct answer is C. \(2ab\). Two \(ab\) strips are removed, so the total subtraction is \(2ab\). Exam tip: \(b^2\) is added back later.
Step 3
Exam Tip
दो \(ab\) पट्टियां हटने से कुल घटाव \(2ab\) होता है। परीक्षा में बाद में \(b^2\) वापस जुड़ता है।
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भुजा \(7+3\) वाले वर्ग का क्षेत्र पहचान द्वारा कितना होगा?
Using the identity, what is the area of a square with side \(7+3\)?
#mental math
#area identity
#numeric model
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A \(100\)
B \(49\)
C \(58\)
D \(79\)
Explanation opens after your attempt
Correct Answer
A. \(100\)
Step 1
Concept
\((7+3)^2=7^2+2\times7\times3+3^2=100\). Exam tip: use identities for mental calculation.
Step 2
Why this answer is correct
The correct answer is A. \(100\). \((7+3)^2=7^2+2\times7\times3+3^2=100\). Exam tip: use identities for mental calculation.
Step 3
Exam Tip
\((7+3)^2=7^2+2\times7\times3+3^2=100\) होता है। परीक्षा में पहचान से मानसिक गणना करें।
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एक चित्र में \(12^2-2\times12\times2+2^2\) दिखाया गया है। यह किस वर्ग का क्षेत्र है?
A diagram shows \(12^2-2\times12\times2+2^2\). It is the area of which square?
#numeric identity
#visual square
#minus model
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A भुजा \(12+2\) / Side \(12+2\)
B भुजा \(12-2\) / Side \(12-2\)
C भुजा \(12\times2\) / Side \(12\times2\)
D भुजा \(12^2\) / Side \(12^2\)
Explanation opens after your attempt
Correct Answer
B. भुजा \(12-2\) / Side \(12-2\)
Step 1
Concept
This is the form of \((12-2)^2\). Exam tip: identify \(a^2-2ab+b^2\) as \((a-b)^2\).
Step 2
Why this answer is correct
The correct answer is B. भुजा \(12-2\) / Side \(12-2\). This is the form of \((12-2)^2\). Exam tip: identify \(a^2-2ab+b^2\) as \((a-b)^2\).
Step 3
Exam Tip
यह \((12-2)^2\) का रूप है। परीक्षा में \(a^2-2ab+b^2\) को \((a-b)^2\) पहचानें।
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यदि \(9^2-4^2\) को दृश्य मॉडल से हल करें, तो कौन सा आयत बनेगा?
If \(9^2-4^2\) is solved using a visual model, which rectangle is formed?
#difference of squares
#numeric visual
#rectangle
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A आयाम \(9+4\) और \(9-4\) / Dimensions \(9+4\) and \(9-4\)
B आयाम \(9\) और \(4\) / Dimensions \(9\) and \(4\)
C आयाम \(9+9\) और \(4+4\) / Dimensions \(9+9\) and \(4+4\)
D आयाम \(9-4\) और \(9-4\) / Dimensions \(9-4\) and \(9-4\)
Explanation opens after your attempt
Correct Answer
A. आयाम \(9+4\) और \(9-4\) / Dimensions \(9+4\) and \(9-4\)
Step 1
Concept
In difference of squares, dimensions become \((a+b)\) and \((a-b)\). Exam tip: compute \(9^2-4^2=(13)(5)\).
Step 2
Why this answer is correct
The correct answer is A. आयाम \(9+4\) और \(9-4\) / Dimensions \(9+4\) and \(9-4\). In difference of squares, dimensions become \((a+b)\) and \((a-b)\). Exam tip: compute \(9^2-4^2=(13)(5)\).
Step 3
Exam Tip
अंतर के वर्गों में आयाम \((a+b)\) और \((a-b)\) बनते हैं। परीक्षा में \(9^2-4^2=(13)(5)\) करें।
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आयत मॉडल में \(x(x+6)\) को किस योग से दिखाया जाता है?
In a rectangle model, \(x(x+6)\) is shown by which sum?
#distributive area
#rectangle model
#algebra
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A \(x^2+36\)
B \(x^2+6x\)
C \(6x^2+x\)
D \(x+6\)
Explanation opens after your attempt
Correct Answer
B. \(x^2+6x\)
Step 1
Concept
Splitting the rectangle into parts with widths \(x\) and \(6\) gives \(x^2+6x\). Exam tip: see distribution as area.
Step 2
Why this answer is correct
The correct answer is B. \(x^2+6x\). Splitting the rectangle into parts with widths \(x\) and \(6\) gives \(x^2+6x\). Exam tip: see distribution as area.
Step 3
Exam Tip
आयत को \(x\) और \(6\) चौड़ाई वाले भागों में बांटने पर \(x^2+6x\) मिलता है। परीक्षा में वितरण को क्षेत्र के रूप में देखें।
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भुजा \(a+b\) वाले वर्ग में कुल कितने आयताकार \(ab\) भाग होते हैं?
How many rectangular \(ab\) parts are there in a square of side \(a+b\)?
#area parts
#ab rectangles
#square model
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A \(1\)
B \(3\)
C \(2\)
D \(4\)
Explanation opens after your attempt
Step 1
Concept
There is one \(ab\) part above and one \(ab\) part beside. Exam tip: add both as \(2ab\).
Step 2
Why this answer is correct
The correct answer is C. \(2\). There is one \(ab\) part above and one \(ab\) part beside. Exam tip: add both as \(2ab\).
Step 3
Exam Tip
एक \(ab\) भाग ऊपर और एक \(ab\) भाग बगल में होता है। परीक्षा में दोनों को जोड़कर \(2ab\) लिखें।
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यदि \(x^2+2xy+y^2\) को टाइलों से बनाया गया है, तो बाहरी भुजा क्या होगी?
If \(x^2+2xy+y^2\) is made with tiles, what will be the outer side?
#algebra tiles
#outer side
#perfect square
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A \(x-y\)
B \(xy\)
C \(2x+y\)
D \(x+y\)
Explanation opens after your attempt
Correct Answer
D. \(x+y\)
Step 1
Concept
These tiles form a square of side \(x+y\). Exam tip: identify the outer side of a perfect square.
Step 2
Why this answer is correct
The correct answer is D. \(x+y\). These tiles form a square of side \(x+y\). Exam tip: identify the outer side of a perfect square.
Step 3
Exam Tip
ये टाइलें मिलकर भुजा \(x+y\) का वर्ग बनाती हैं। परीक्षा में पूर्ण वर्ग की बाहरी भुजा पहचानें।
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एक वर्ग मॉडल में \(x^2\), दो \(2x\) आयत और \(4\) इकाई वर्ग हैं। पहचान कौन सी है?
A square model has \(x^2\), two \(2x\) rectangles, and \(4\) unit squares. Which identity is it?
#square tile
#binomial expansion
#visual model
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A \((x+2)^2=x^2+4x+4\)
B \((x-2)^2=x^2-4x+4\)
C \(x^2-4=(x+2)(x-2)\)
D \(x^2+2x+4\)
Explanation opens after your attempt
Correct Answer
A. \((x+2)^2=x^2+4x+4\)
Step 1
Concept
Two \(2x\) rectangles make \(4x\), and \(2^2=4\). Exam tip: check the side of the small square.
Step 2
Why this answer is correct
The correct answer is A. \((x+2)^2=x^2+4x+4\). Two \(2x\) rectangles make \(4x\), and \(2^2=4\). Exam tip: check the side of the small square.
Step 3
Exam Tip
दो \(2x\) आयतों से \(4x\) बनता है और \(2^2=4\) है। परीक्षा में छोटे वर्ग की भुजा देखें।
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कौन सा कथन क्षेत्र मॉडल के लिए सही है?
Which statement is correct for an area model?
#area model
#concept
#visual algebra
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A क्षेत्र मॉडल में लंबाई और चौड़ाई का गुणन प्रयोग होता है / Area model uses multiplication of length and breadth
B क्षेत्र मॉडल में केवल भाग देना होता है / Area model uses only division
C क्षेत्र मॉडल में चिह्नों का कोई महत्व नहीं होता / Signs have no importance in area models
D क्षेत्र मॉडल में सभी पद हटाए जाते हैं / All terms are removed in area models
Explanation opens after your attempt
Correct Answer
A. क्षेत्र मॉडल में लंबाई और चौड़ाई का गुणन प्रयोग होता है / Area model uses multiplication of length and breadth
Step 1
Concept
An area model shows multiplication and addition in a diagram. Exam tip: take area as length times breadth.
Step 2
Why this answer is correct
The correct answer is A. क्षेत्र मॉडल में लंबाई और चौड़ाई का गुणन प्रयोग होता है / Area model uses multiplication of length and breadth. An area model shows multiplication and addition in a diagram. Exam tip: take area as length times breadth.
Step 3
Exam Tip
क्षेत्र मॉडल गुणन और जोड़ को चित्र में दिखाता है। परीक्षा में क्षेत्र को लंबाई गुणा चौड़ाई मानें।
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\((m+4)^2\) के दृश्य मॉडल में छोटे वर्ग का क्षेत्र क्या होगा?
In the visual model of \((m+4)^2\), what is the area of the small square?
#small square
#area model
#binomial square
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A \(m^2\)
B \(16\)
C \(4m\)
D \(8m\)
Explanation opens after your attempt
Step 1
Concept
The small square has side \(4\), so its area is \(4^2=16\). Exam tip: square the constant number.
Step 2
Why this answer is correct
The correct answer is B. \(16\). The small square has side \(4\), so its area is \(4^2=16\). Exam tip: square the constant number.
Step 3
Exam Tip
छोटे वर्ग की भुजा \(4\) है, इसलिए उसका क्षेत्र \(4^2=16\) है। परीक्षा में स्थिर संख्या का वर्ग करें।
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\((a+2)(a+5)\) के आयत मॉडल में स्थिर कोने का क्षेत्र कितना होगा?
In the rectangle model of \((a+2)(a+5)\), what will be the area of the constant corner?
#rectangle model
#constant term
#visual expansion
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A \(2\)
B \(5\)
C \(10\)
D \(7\)
Explanation opens after your attempt
Step 1
Concept
The constant corner is formed by \(2\times5=10\). Exam tip: connect the final constant term with the corner area.
Step 2
Why this answer is correct
The correct answer is C. \(10\). The constant corner is formed by \(2\times5=10\). Exam tip: connect the final constant term with the corner area.
Step 3
Exam Tip
स्थिर कोना \(2\times5=10\) से बनता है। परीक्षा में अंतिम स्थिर पद को कोने के क्षेत्र से जोड़ें।
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दृश्य मॉडल में \((x+1)(x+4)\) का बीच वाला \(x\) पद किससे बनता है?
In the visual model of \((x+1)(x+4)\), how is the middle \(x\) term formed?
#middle term
#rectangle parts
#visual multiplication
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A \(1x+4x\) से / From \(1x+4x\)
B \(1+4\) से / From \(1+4\)
C \(x^2+4\) से / From \(x^2+4\)
D \(x\times x\) से / From \(x\times x\)
Explanation opens after your attempt
Correct Answer
A. \(1x+4x\) से / From \(1x+4x\)
Step 1
Concept
Two rectangular parts \(x\) and \(4x\) combine to make \(5x\). Exam tip: add the \(x\)-terms.
Step 2
Why this answer is correct
The correct answer is A. \(1x+4x\) से / From \(1x+4x\). Two rectangular parts \(x\) and \(4x\) combine to make \(5x\). Exam tip: add the \(x\)-terms.
Step 3
Exam Tip
दो आयताकार भाग \(x\) और \(4x\) मिलकर \(5x\) बनाते हैं। परीक्षा में \(x\) वाले पद जोड़ें।
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किस अभिव्यक्ति को भुजा \(u-v\) वाले वर्ग के क्षेत्र से दिखाया जा सकता है?
Which expression can be shown by the area of a square with side \(u-v\)?
#minus binomial
#area square
#visual identity
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A \(u^2-v^2\)
B \(u^2-2uv+v^2\)
C \(u^2+2uv+v^2\)
D \(uv-u-v\)
Explanation opens after your attempt
Correct Answer
B. \(u^2-2uv+v^2\)
Step 1
Concept
The square area is \((u-v)^2\), which becomes \(u^2-2uv+v^2\). Exam tip: keep the middle term negative.
Step 2
Why this answer is correct
The correct answer is B. \(u^2-2uv+v^2\). The square area is \((u-v)^2\), which becomes \(u^2-2uv+v^2\). Exam tip: keep the middle term negative.
Step 3
Exam Tip
वर्ग का क्षेत्र \((u-v)^2\) है जो \(u^2-2uv+v^2\) बनता है। परीक्षा में बीच का पद ऋणात्मक रखें।
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यदि \(15^2-5^2\) को आयत में बदला जाए, तो क्षेत्र कितना होगा?
If \(15^2-5^2\) is changed into a rectangle, what will be the area?
#numeric difference
#visual rectangle
#identity
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A \(100\)
B \(150\)
C \(200\)
D \(250\)
Explanation opens after your attempt
Correct Answer
C. \(200\)
Step 1
Concept
\(15^2-5^2=(15+5)(15-5)=20\times10=200\). Exam tip: calculate quickly using difference of squares.
Step 2
Why this answer is correct
The correct answer is C. \(200\). \(15^2-5^2=(15+5)(15-5)=20\times10=200\). Exam tip: calculate quickly using difference of squares.
Step 3
Exam Tip
\(15^2-5^2=(15+5)(15-5)=20\times10=200\) है। परीक्षा में अंतर के वर्गों से तेज गणना करें।
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पूर्ण वर्ग बनाने के लिए \(x^2+8x\) के क्षेत्र मॉडल में कौन सा छोटा वर्ग जोड़ना चाहिए?
Which small square should be added in the area model of \(x^2+8x\) to make a complete square?
#complete square
#area completion
#visual identity
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A क्षेत्र \(8\) का वर्ग / Square of area \(8\)
B क्षेत्र \(12\) का वर्ग / Square of area \(12\)
C क्षेत्र \(64\) का वर्ग / Square of area \(64\)
D क्षेत्र \(16\) का वर्ग / Square of area \(16\)
Explanation opens after your attempt
Correct Answer
D. क्षेत्र \(16\) का वर्ग / Square of area \(16\)
Step 1
Concept
\(8x\) splits into two equal \(4x\) rectangles, so \(4^2=16\) is added. Exam tip: square half the coefficient.
Step 2
Why this answer is correct
The correct answer is D. क्षेत्र \(16\) का वर्ग / Square of area \(16\). \(8x\) splits into two equal \(4x\) rectangles, so \(4^2=16\) is added. Exam tip: square half the coefficient.
Step 3
Exam Tip
\(8x\) दो बराबर \(4x\) आयतों में बंटता है, इसलिए \(4^2=16\) जोड़ा जाता है। परीक्षा में आधे गुणांक का वर्ग करें।
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कौन सा मॉडल \((a+b+c)^2\) में \(2ab\), \(2bc\) और \(2ca\) बनने को समझाता है?
Which model explains the formation of \(2ab\), \(2bc\), and \(2ca\) in \((a+b+c)^2\)?
#three part square
#visual expansion
#area model
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A तीन भागों में बंटा वर्ग / A square divided into three parts
B एक सीधी रेखा / A straight line
C एक वृत्त / A circle
D एक त्रिभुज / A triangle
Explanation opens after your attempt
Correct Answer
A. तीन भागों में बंटा वर्ग / A square divided into three parts
Step 1
Concept
A square divided into three parts creates two equal rectangles for each pair. Exam tip: double the paired rectangles.
Step 2
Why this answer is correct
The correct answer is A. तीन भागों में बंटा वर्ग / A square divided into three parts. A square divided into three parts creates two equal rectangles for each pair. Exam tip: double the paired rectangles.
Step 3
Exam Tip
तीन भागों वाला वर्ग हर दो भागों के दो बराबर आयत बनाता है। परीक्षा में जोड़ीदार आयतों को दोगुना करें।
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भुजा \(20-1\) वाले वर्ग का क्षेत्र पहचान से क्या होगा?
Using identity, what is the area of a square with side \(20-1\)?
#mental calculation
#minus square
#visual identity
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A \(399\)
B \(361\)
C \(381\)
D \(421\)
Explanation opens after your attempt
Correct Answer
B. \(361\)
Step 1
Concept
\((20-1)^2=400-40+1=361\). Exam tip: use the subtraction model from the nearby large number.
Step 2
Why this answer is correct
The correct answer is B. \(361\). \((20-1)^2=400-40+1=361\). Exam tip: use the subtraction model from the nearby large number.
Step 3
Exam Tip
\((20-1)^2=400-40+1=361\) होता है। परीक्षा में पास की बड़ी संख्या से घटाव मॉडल अपनाएं।
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किस स्थिति में क्षेत्र मॉडल में \(2ab\) का पद दिखाई नहीं देगा?
In which situation will the term \(2ab\) not appear in the area model?
#difference model
#area identity
#no middle term
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A जब भुजा \(a+b\) हो / When the side is \(a+b\)
B जब भुजा \(a-b\) हो / When the side is \(a-b\)
C जब क्षेत्र \(a^2-b^2\) को आयत \((a+b)(a-b)\) से दिखाएं / When area \(a^2-b^2\) is shown by rectangle \((a+b)(a-b)\)
D जब दो \(ab\) आयत हों / When there are two \(ab\) rectangles
Explanation opens after your attempt
Correct Answer
C. जब क्षेत्र \(a^2-b^2\) को आयत \((a+b)(a-b)\) से दिखाएं / When area \(a^2-b^2\) is shown by rectangle \((a+b)(a-b)\)
Step 1
Concept
In the rectangle model of \(a^2-b^2\), the middle \(2ab\) term does not appear. Exam tip: connect each identity with its own model.
Step 2
Why this answer is correct
The correct answer is C. जब क्षेत्र \(a^2-b^2\) को आयत \((a+b)(a-b)\) से दिखाएं / When area \(a^2-b^2\) is shown by rectangle \((a+b)(a-b)\). In the rectangle model of \(a^2-b^2\), the middle \(2ab\) term does not appear. Exam tip: connect each identity with its own model.
Step 3
Exam Tip
\(a^2-b^2\) के आयत मॉडल में बीच का \(2ab\) पद रद्द रूप में नहीं आता। परीक्षा में अलग पहचान को अलग मॉडल से जोड़ें।
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एक \(x+6\) भुजा वाले वर्ग में दो समान आयतों का कुल क्षेत्र क्या होगा?
In a square of side \(x+6\), what will be the total area of the two equal rectangles?
#equal rectangles
#binomial square
#area model
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A \(6x\)
B \(12x\)
C \(36x\)
D \(x^2\)
Explanation opens after your attempt
Correct Answer
B. \(12x\)
Step 1
Concept
The two rectangles have areas \(6x\) and \(6x\), so the total is \(12x\). Exam tip: double equal rectangles.
Step 2
Why this answer is correct
The correct answer is B. \(12x\). The two rectangles have areas \(6x\) and \(6x\), so the total is \(12x\). Exam tip: double equal rectangles.
Step 3
Exam Tip
दोनों आयतों का क्षेत्र \(6x\) और \(6x\) है, इसलिए कुल \(12x\) है। परीक्षा में समान आयतों को दोगुना करें।
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यदि किसी वर्ग मॉडल का कुल क्षेत्र \(x^2+14x+49\) है, तो उसकी भुजा क्या होगी?
If the total area of a square model is \(x^2+14x+49\), what will be its side?
#perfect square
#side identification
#visual model
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A \(x+49\)
B \(x+14\)
C \(x+7\)
D \(x-7\)
Explanation opens after your attempt
Correct Answer
C. \(x+7\)
Step 1
Concept
\(49=7^2\) and \(14x=2\times7\times x\). Exam tip: identify the side from the square root of the last term.
Step 2
Why this answer is correct
The correct answer is C. \(x+7\). \(49=7^2\) and \(14x=2\times7\times x\). Exam tip: identify the side from the square root of the last term.
Step 3
Exam Tip
\(49=7^2\) और \(14x=2\times7\times x\) है। परीक्षा में अंतिम पद की वर्गमूल से भुजा पहचानें।
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किस दृश्य मॉडल में चारों कोनों को जोड़कर एक बड़ा वर्ग बनता है जिसकी भुजा \(a+b\) होती है?
In which visual model do the parts combine to form a larger square with side \(a+b\)?
#large square
#visual identity
#binomial model
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A \((a-b)^2\) का मॉडल / Model of \((a-b)^2\)
B \((a+b)^2\) का मॉडल / Model of \((a+b)^2\)
C \(a^2-b^2\) का मॉडल / Model of \(a^2-b^2\)
D \(ab\) का मॉडल / Model of \(ab\)
Explanation opens after your attempt
Correct Answer
B. \((a+b)^2\) का मॉडल / Model of \((a+b)^2\)
Step 1
Concept
In \((a+b)^2\), all parts form a large square without gaps. Exam tip: read the outer side first.
Step 2
Why this answer is correct
The correct answer is B. \((a+b)^2\) का मॉडल / Model of \((a+b)^2\). In \((a+b)^2\), all parts form a large square without gaps. Exam tip: read the outer side first.
Step 3
Exam Tip
\((a+b)^2\) में सभी भाग बिना खाली जगह के बड़ा वर्ग बनाते हैं। परीक्षा में बाहरी भुजा को पहले पढ़ें।
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क्षेत्र मॉडल में पहचान सीखने का मुख्य लाभ क्या है?
What is the main benefit of learning identities through an area model?
#concept clarity
#visual model
#algebraic identities
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A सूत्रों को केवल याद करना पड़ता है / Formulas only need to be memorized
B गलत उत्तर जल्दी छिप जाते हैं / Wrong answers hide quickly
C पदों का आकार और अर्थ साफ दिखाई देता है / The shape and meaning of terms become clear
D गुणा की जरूरत नहीं रहती / Multiplication is not needed
Explanation opens after your attempt
Correct Answer
C. पदों का आकार और अर्थ साफ दिखाई देता है / The shape and meaning of terms become clear
Step 1
Concept
A visual model helps us understand the area of each term. Exam tip: verify the formula through the diagram.
Step 2
Why this answer is correct
The correct answer is C. पदों का आकार और अर्थ साफ दिखाई देता है / The shape and meaning of terms become clear. A visual model helps us understand the area of each term. Exam tip: verify the formula through the diagram.
Step 3
Exam Tip
दृश्य मॉडल से हर पद का क्षेत्र समझ में आता है। परीक्षा में चित्र से सूत्र की पुष्टि करें।
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