(a+b+c) वर्ग मॉडल में मिश्रित आयतों का कुल क्षेत्रफल क्या होगा?
In the square model of (a+b+c), what is the total area of the mixed rectangles?
#mixed-rectangles
#three-term-square
#area
A (ab+bc+ca)
B (2ab+2bc+2ca)
C \(a^2+b^2+c^2\)
D (3abc)
Explanation opens after your attempt
Correct Answer
B. (2ab+2bc+2ca)
Step 1
Concept
Each pair has two rectangles, so the total is (2ab+2bc+2ca). In exams, count each mixed pair twice.
Step 2
Why this answer is correct
The correct answer is B. (2ab+2bc+2ca). Each pair has two rectangles, so the total is (2ab+2bc+2ca). In exams, count each mixed pair twice.
Step 3
Exam Tip
हर जोड़ी के दो आयत होते हैं इसलिए कुल (2ab+2bc+2ca) है। परीक्षा में हर मिश्रित जोड़ी दो बार गिनें।
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एक तीन-भाग वर्ग मॉडल में भुजा (a+b+c) है। केवल छोटे वर्गों का कुल क्षेत्रफल क्या होगा?
In a three-part square model, the side is (a+b+c). What is the total area of only the small squares?
#three-term-square
#small-squares
#visual
A \(a^2+b^2+c^2\)
B (ab+bc+ca)
C (2ab+2bc+2ca)
D (a+b+c)
Explanation opens after your attempt
Correct Answer
A. \(a^2+b^2+c^2\)
Step 1
Concept
The small squares have sides (a), (b), and (c). In exams, distinguish square parts from rectangle parts.
Step 2
Why this answer is correct
The correct answer is A. \(a^2+b^2+c^2\). The small squares have sides (a), (b), and (c). In exams, distinguish square parts from rectangle parts.
Step 3
Exam Tip
छोटे वर्गों की भुजाएँ (a), (b) और (c) हैं। परीक्षा में वर्ग और आयत भाग अलग पहचानें।
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दृश्य मॉडल में ((a+b+c)2 ) के वर्गीय भाग कौन से हैं?
In the visual model of ((a+b+c)2 ), which are the square parts?
#three-term-square
#square-parts
#visual-model
A \(a^2\), \(b^2\), \(c^2\)
B (ab), (bc), (ca)
C (2ab), (2bc), (2ca)
D (a+b+c)
Explanation opens after your attempt
Correct Answer
A. \(a^2\), \(b^2\), \(c^2\)
Step 1
Concept
Each of the three side parts forms its own square. Exam tip: distinguish square parts and rectangular parts.
Step 2
Why this answer is correct
The correct answer is A. \(a^2\), \(b^2\), \(c^2\). Each of the three side parts forms its own square. Exam tip: distinguish square parts and rectangular parts.
Step 3
Exam Tip
तीनों अलग भुजा भागों के अपने-अपने वर्ग बनते हैं। परीक्षा में वर्गीय भाग और आयताकार भाग अलग पहचानें।
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भुजा (a+b+c) वाले वर्ग के दृश्य मॉडल में (bc) आयत कितनी बार आएगा?
In the visual model of a square with side (a+b+c), how many times will the (bc) rectangle appear?
#three-term-square
#pair-rectangles
#visual-counting
A एक बार / Once
B दो बार / Twice
C तीन बार / Thrice
D छह बार / Six times
Explanation opens after your attempt
Correct Answer
B. दो बार / Twice
Step 1
Concept
Each different pair forms two equal rectangles, so (bc) appears twice. Exam tip: count paired rectangles.
Step 2
Why this answer is correct
The correct answer is B. दो बार / Twice. Each different pair forms two equal rectangles, so (bc) appears twice. Exam tip: count paired rectangles.
Step 3
Exam Tip
हर अलग जोड़ी के दो समान आयत बनते हैं इसलिए (bc) दो बार आता है। परीक्षा में जोड़ीदार आयत गिनें।
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भुजा (a+b+c) वाले वर्ग को (3) भागों में दोनों दिशाओं में बांटने पर कुल कितने छोटे क्षेत्र बनेंगे?
When a square of side (a+b+c) is divided into (3) parts in both directions, how many small regions are formed?
#three term square
#grid model
#visual identity
A (3)
B (6)
C (9)
D (12)
Explanation opens after your attempt
Step 1
Concept
Three rows and three columns make \(3\cdot3=9\) regions. Exam tip: multiply rows and columns.
Step 2
Why this answer is correct
The correct answer is C. (9). Three rows and three columns make \(3\cdot3=9\) regions. Exam tip: multiply rows and columns.
Step 3
Exam Tip
तीन पंक्तियां और तीन स्तंभ मिलकर \(3\cdot3=9\) क्षेत्र बनाते हैं। परीक्षा में पंक्तियों और स्तंभों को गुणा करें।
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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
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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यदि ( (a+b+c)2 ) के दृश्य मॉडल में \(a^2+b^2+c^2\) और (2ab+2bc) दिख रहा है, तो कौन-सा भाग छूटा है?
If the model of ( (a+b+c)2 ) shows \(a^2+b^2+c^2\) and (2ab+2bc), which part is missing?
#missing-part
#three-term-square
#visual
A (ab+bc+ca)
B (abc)
C (2ca)
D (a+b+c)
Explanation opens after your attempt
Step 1
Concept
Among the three mixed pairs, the (ca) pair also appears twice. In exams, complete all pair combinations.
Step 2
Why this answer is correct
The correct answer is C. (2ca). Among the three mixed pairs, the (ca) pair also appears twice. In exams, complete all pair combinations.
Step 3
Exam Tip
तीन मिश्रित जोड़ियों में (ca) जोड़ी भी दो बार आती है। परीक्षा में सभी जोड़ी संयोजन पूरे करें।
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यदि ( (x+y+z)2 ) के क्षेत्रफल मॉडल में केवल वर्गों का योग घटा दिया जाए, तो क्या बचेगा?
If the sum of only the squares is removed from the area model of ( (x+y+z)2 ), what remains?
#three-term-square
#mixed-area
#visual
A (2xy+2yz+2zx)
B (xy+yz+zx)
C (x+y+z)
D (3xyz)
Explanation opens after your attempt
Correct Answer
A. (2xy+2yz+2zx)
Step 1
Concept
After removing the squares, only six mixed rectangles remain. In exams, add them as (2xy+2yz+2zx).
Step 2
Why this answer is correct
The correct answer is A. (2xy+2yz+2zx). After removing the squares, only six mixed rectangles remain. In exams, add them as (2xy+2yz+2zx).
Step 3
Exam Tip
वर्ग हटाने पर केवल छह मिश्रित आयत बचते हैं। परीक्षा में उन्हें (2xy+2yz+2zx) के रूप में जोड़ें।
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यदि (a+b+c) भुजा वाले वर्ग को तीन भागों में काटकर मॉडल बनाया जाए, तो (ab) प्रकार के कितने आयत होंगे?
If a square of side (a+b+c) is cut into three parts to make a model, how many rectangles of type (ab) will appear?
#three-term-square
#area-count
#visual
A (1)
B (2)
C (3)
D (6)
Explanation opens after your attempt
Step 1
Concept
(ab) and (ba) appear as two different rectangles. In exams, count each pair twice.
Step 2
Why this answer is correct
The correct answer is B. (2). (ab) and (ba) appear as two different rectangles. In exams, count each pair twice.
Step 3
Exam Tip
(ab) और (ba) दो अलग आयतों में दिखते हैं। परीक्षा में हर जोड़ी को दो बार गिनें।
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भुजा (a+b+c) वाले वर्ग को दृश्य मॉडल में बांटने पर कौन-सा क्षेत्रफल विस्तार सही है?
When a square of side (a+b+c) is partitioned in a visual model, which area expansion is correct?
#three term square
#visual model
#area partition
A \(a^2+b^2+c^2+ab+bc+ca\) / one set of rectangles
B \(a^2+b^2+c^2+2ab+2bc+2ca\) / complete partition
C \(a^2+b^2+c^2+3abc\) / volume-like term
D \(a^2+b^2+c^2+2abc\) / alternate dimension
Explanation opens after your attempt
Correct Answer
B. \(a^2+b^2+c^2+2ab+2bc+2ca\) / complete partition
Step 1
Concept
Three squares and six rectangles make \(a^2+b^2+c^2+2ab+2bc+2ca\). In exams count each pair of rectangles.
Step 2
Why this answer is correct
The correct answer is B. \(a^2+b^2+c^2+2ab+2bc+2ca\) / complete partition. Three squares and six rectangles make \(a^2+b^2+c^2+2ab+2bc+2ca\). In exams count each pair of rectangles.
Step 3
Exam Tip
तीन वर्ग और छह आयत मिलकर \(a^2+b^2+c^2+2ab+2bc+2ca\) बनाते हैं। परीक्षा में हर आयत की जोड़ी गिनें।
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दृश्य मॉडल में ((a+b+c)2 ) के कुल आयताकार क्रॉस भाग कितने होते हैं?
In the visual model of ((a+b+c)2 ), how many rectangular cross parts are there in total?
#three-term-square
#cross-rectangles
#visual-counting
A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
There are three pairs (ab), (bc), (ca), and each pair has two rectangles. Exam tip: multiply (3) pairs by (2).
Step 2
Why this answer is correct
The correct answer is D. (6). There are three pairs (ab), (bc), (ca), and each pair has two rectangles. Exam tip: multiply (3) pairs by (2).
Step 3
Exam Tip
तीन जोड़े (ab), (bc), (ca) होते हैं और हर जोड़े के दो आयत होते हैं। परीक्षा में (3) जोड़ों को (2) से गुणा करें।
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भुजा (x+y+z) वाले वर्ग में (xy) वाले आयत कितनी बार दिखाई देंगे?
In a square of side (x+y+z), how many times will rectangles of area (xy) appear?
#three-term-square
#pair-rectangles
#visual-model
A एक बार / Once
B दो बार / Twice
C तीन बार / Thrice
D चार बार / Four times
Explanation opens after your attempt
Correct Answer
B. दो बार / Twice
Step 1
Concept
The pair (x) and (y) forms two equal (xy) rectangles. Exam tip: count two rectangles for each different pair.
Step 2
Why this answer is correct
The correct answer is B. दो बार / Twice. The pair (x) and (y) forms two equal (xy) rectangles. Exam tip: count two rectangles for each different pair.
Step 3
Exam Tip
(x) और (y) के जोड़े से दो समान आयत (xy) बनते हैं। परीक्षा में प्रत्येक अलग जोड़ी के लिए दो आयत गिनें।
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एक (a+b+c) भुजा वाले वर्ग का पूरा क्षेत्रफल किस विस्तार से दिखेगा?
Which expansion shows the full area of a square with side (a+b+c)?
#three term square
#visual expansion
#area model
A \(a^2+b^2+c^2+ab+bc+ca\)
B \(a^2+b^2+c^2+2ab+2bc+2ca\)
C \(a^2+b^2+c^2-2ab-2bc-2ca\)
D \(a^2+b^2+c^2+3abc\)
Explanation opens after your attempt
Correct Answer
B. \(a^2+b^2+c^2+2ab+2bc+2ca\)
Step 1
Concept
Three squares and six cross rectangles give \(a^2+b^2+c^2+2ab+2bc+2ca\). Exam tip: multiply equal pairs by (2).
Step 2
Why this answer is correct
The correct answer is B. \(a^2+b^2+c^2+2ab+2bc+2ca\). Three squares and six cross rectangles give \(a^2+b^2+c^2+2ab+2bc+2ca\). Exam tip: multiply equal pairs by (2).
Step 3
Exam Tip
तीन वर्ग और छह क्रॉस आयत मिलकर \(a^2+b^2+c^2+2ab+2bc+2ca\) देते हैं। परीक्षा में समान जोड़ों को (2) से गुणा करें।
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एक मॉडल में (a+b+c) भुजा वाले वर्ग को (3) भागों में दोनों दिशाओं में बांटा गया है। (ab) से संबंधित कुल क्षेत्रफल कौन सा होगा?
In a model, a square of side (a+b+c) is divided into (3) parts in both directions. What is the total area related to (ab)?
#three term square
#area grid
#cross terms
A (ab)
B (2ab)
C (3ab)
D \(a^2+b^2\)
Explanation opens after your attempt
Step 1
Concept
The grid contains two equal rectangles (ab) and (ba). Therefore the related total area is (2ab).
Step 2
Why this answer is correct
The correct answer is B. (2ab). The grid contains two equal rectangles (ab) and (ba). Therefore the related total area is (2ab).
Step 3
Exam Tip
ग्रिड में (ab) और (ba) दो समान आयत होते हैं। इसलिए संबंधित कुल क्षेत्रफल (2ab) है।
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(a+b+c) भुजा वाले वर्ग में छोटे वर्गों के क्षेत्रफल कौन-से होंगे?
In a square of side (a+b+c), what will be the areas of the small squares?
#three-term-square
#small-squares
#visual
A \(a^2\), \(b^2\), \(c^2\)
B (ab), (bc), (ca)
C (2ab), (2bc), (2ca)
D (abc), (a+b+c), (1)
Explanation opens after your attempt
Correct Answer
A. \(a^2\), \(b^2\), \(c^2\)
Step 1
Concept
Each small square has side (a), (b), (c) respectively. In exams, distinguish square and rectangle parts.
Step 2
Why this answer is correct
The correct answer is A. \(a^2\), \(b^2\), \(c^2\). Each small square has side (a), (b), (c) respectively. In exams, distinguish square and rectangle parts.
Step 3
Exam Tip
हर छोटे वर्ग की भुजा क्रमशः (a), (b), (c) है। परीक्षा में वर्ग और आयत भाग अलग पहचानें।
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एक मॉडल में (a+b+c) भुजा वाले वर्ग को अलग भागों में बाँटा गया। कुल क्षेत्रफल में कौन-सा पद अवश्य आएगा?
A model divides a square of side (a+b+c) into parts. Which term must appear in the total area?
#three-term-square
#visual-model
#area
A ( 2ab+2bc+2ca )
B ( ab+bc+ca )
C \( a^2+b^2+c^2 \) ही / Only \( a^2+b^2+c^2 \)
D ( 3abc )
Explanation opens after your attempt
Correct Answer
A. ( 2ab+2bc+2ca )
Step 1
Concept
Because of three pairs of rectangles, (2ab), (2bc) and (2ca) appear. In exams, count each pair twice.
Step 2
Why this answer is correct
The correct answer is A. ( 2ab+2bc+2ca ). Because of three pairs of rectangles, (2ab), (2bc) and (2ca) appear. In exams, count each pair twice.
Step 3
Exam Tip
तीन जोड़ी आयतों के कारण (2ab), (2bc) और (2ca) आते हैं। परीक्षा में हर जोड़ी दो बार गिनें।
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यदि (a+b+c=9) और (ab+bc+ca=20) है तो \(a^2+b^2+c^2\) कितना होगा?
If (a+b+c=9) and (ab+bc+ca=20), what is \(a^2+b^2+c^2\)?
#three term square
#given values
#sum of squares
A (41)
B (49)
C (61)
D (81)
Explanation opens after your attempt
Step 1
Concept
(a-2 +b-2 +c-2 =(a+b+c)2 -2(ab+bc+ca)=81-40=41). Exam tip: directly use the square identity of three terms.
Step 2
Why this answer is correct
The correct answer is A. (41). (a-2 +b-2 +c-2 =(a+b+c)2 -2(ab+bc+ca)=81-40=41). Exam tip: directly use the square identity of three terms.
Step 3
Exam Tip
(a-2 +b-2 +c-2 =(a+b+c)2 -2(ab+bc+ca)=81-40=41)। परीक्षा में तीन पदों की वर्ग पहचान सीधे लगाएँ।
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( (2x+3y+4)2 ) में (xy), (x) और (y) वाले पदों का योग क्या है?
What is the sum of the terms containing (xy), (x), and (y) in ( (2x+3y+4)2 )?
#three term square
#pair products
#constant term
A (12xy+16x+24y) / सही योग
B (6xy+8x+12y) / आधा परिणाम
C (24xy+16x+12y) / (xy) पद गलत
D \(4x^2+9y^2+16\) / वर्ग पद
Explanation opens after your attempt
Correct Answer
A. (12xy+16x+24y) / सही योग
Step 1
Concept
The pair terms are \(2\cdot2x\cdot3y=12xy\), \(2\cdot2x\cdot4=16x\), and \(2\cdot3y\cdot4=24y\).
Step 2
Why this answer is correct
The correct answer is A. (12xy+16x+24y) / सही योग. The pair terms are \(2\cdot2x\cdot3y=12xy\), \(2\cdot2x\cdot4=16x\), and \(2\cdot3y\cdot4=24y\).
Step 3
Exam Tip
जोड़ी पद \(2\cdot2x\cdot3y=12xy\), \(2\cdot2x\cdot4=16x\), और \(2\cdot3y\cdot4=24y\) हैं।
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( (3a+b+c)2 -\(9a^2+b^2+c^2\) ) को सरल करने पर क्या मिलेगा?
What is obtained by simplifying ( (3a+b+c)2 -\(9a^2+b^2+c^2\) )?
#three term square
#remaining terms
#expert
A (3ab+3ac+bc) / आधा परिणाम
B (6ab+6ac+2bc) / सही रूप
C (9abc) / तीनों का गुणन
D (0) / गुणन पद बचते हैं
Explanation opens after your attempt
Correct Answer
B. (6ab+6ac+2bc) / सही रूप
Step 1
Concept
The pair terms in the square are (6ab), (6ac), and (2bc). Exam tip: take the double product of every pair.
Step 2
Why this answer is correct
The correct answer is B. (6ab+6ac+2bc) / सही रूप. The pair terms in the square are (6ab), (6ac), and (2bc). Exam tip: take the double product of every pair.
Step 3
Exam Tip
तीन पदों के वर्ग में जोड़ी पद (6ab), (6ac), और (2bc) आते हैं। परीक्षा में हर जोड़ी का दोहरा गुणन करें।
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( (3p+2q+r)2 ) में (pq), (pr) और (qr) वाले पदों का योग क्या होगा?
What is the sum of the terms containing (pq), (pr), and (qr) in ( (3p+2q+r)2 )?
#three term square
#double products
#pair terms
A (6pq+3pr+2qr) / आधा परिणाम
B (12pq+6pr+4qr) / सही योग
C (6pqr) / तीनों का गुणन
D \(9p^2+4q^2+r^2\) / वर्ग पद
Explanation opens after your attempt
Correct Answer
B. (12pq+6pr+4qr) / सही योग
Step 1
Concept
A three-term square has double products of every pair. Here the (pq), (pr), and (qr) terms are (12pq), (6pr), and (4qr).
Step 2
Why this answer is correct
The correct answer is B. (12pq+6pr+4qr) / सही योग. A three-term square has double products of every pair. Here the (pq), (pr), and (qr) terms are (12pq), (6pr), and (4qr).
Step 3
Exam Tip
तीन पदों के वर्ग में हर जोड़ी का दोहरा गुणन आता है। यहाँ (pq), (pr), (qr) पद क्रमशः (12pq), (6pr), (4qr) हैं।
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( (2x-3y+z)2 ) में (xz) वाला पद क्या है?
What is the term containing (xz) in ( (2x-3y+z)2 )?
#three term square
#xz term
#coefficients
A (2xz)
B (4xz)
C (-6xz)
D (6xz)
Explanation opens after your attempt
Step 1
Concept
\(2\times2x\times z=4xz\). Exam tip: find the mixed term for the required pair only.
Step 2
Why this answer is correct
The correct answer is B. (4xz). \(2\times2x\times z=4xz\). Exam tip: find the mixed term for the required pair only.
Step 3
Exam Tip
\(2\times2x\times z=4xz\) मिलता है। परीक्षा में जिस जोड़ी की बात हो वही मिश्र पद निकालें।
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( (a+2b-c)2 ) में (bc) वाला पद कौन सा होगा?
Which term containing (bc) appears in ( (a+2b-c)2 )?
#three term square
#negative mixed term
#bc
A (2bc)
B (-2bc)
C (-4bc)
D (4bc)
Explanation opens after your attempt
Step 1
Concept
\(2\times2b\times(-c)=-4bc\). Exam tip: handle signs carefully in squares of three terms.
Step 2
Why this answer is correct
The correct answer is C. (-4bc). \(2\times2b\times(-c)=-4bc\). Exam tip: handle signs carefully in squares of three terms.
Step 3
Exam Tip
\(2\times2b\times(-c)=-4bc\) है। परीक्षा में तीन पदों के वर्ग में चिन्हों को ध्यान से रखें।
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( (x+y+z)2 ) में \(x^2+y^2+z^2\) हटाने पर क्या बचेगा?
What remains when \(x^2+y^2+z^2\) is removed from ( (x+y+z)2 )?
#three term square
#mixed terms
#identity
A (xy+yz+zx)
B (2xy+2yz+2zx)
C (xyz)
D (x+y+z)
Explanation opens after your attempt
Correct Answer
B. (2xy+2yz+2zx)
Step 1
Concept
The extra mixed terms in the square of three terms are (2xy+2yz+2zx). Exam tip: write all three mixed terms.
Step 2
Why this answer is correct
The correct answer is B. (2xy+2yz+2zx). The extra mixed terms in the square of three terms are (2xy+2yz+2zx). Exam tip: write all three mixed terms.
Step 3
Exam Tip
तीन पदों के वर्ग में अतिरिक्त मिश्र पद (2xy+2yz+2zx) होते हैं। परीक्षा में सभी तीन मिश्र पद लिखें।
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यदि (x+y+z=6) और (xy+yz+zx=11) है तो \(x^2+y^2+z^2\) कितना है?
If (x+y+z=6) and (xy+yz+zx=11), what is \(x^2+y^2+z^2\)?
#three term square
#given values
#sum of squares
A (14)
B (25)
C (36)
D (47)
Explanation opens after your attempt
Step 1
Concept
(x-2 +y-2 +z-2 =(x+y+z)2 -2(xy+yz+zx)=36-22=14). Exam tip: use the three-term identity.
Step 2
Why this answer is correct
The correct answer is A. (14). (x-2 +y-2 +z-2 =(x+y+z)2 -2(xy+yz+zx)=36-22=14). Exam tip: use the three-term identity.
Step 3
Exam Tip
(x-2 +y-2 +z-2 =(x+y+z)2 -2(xy+yz+zx)=36-22=14)। परीक्षा में तीन पदों की पहचान उपयोग करें।
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( (2a-b+4c)2 ) में (ab) वाला पद क्या है?
What is the term containing (ab) in ( (2a-b+4c)2 )?
#three term square
#negative mixed term
#coefficients
A (2ab)
B (-2ab)
C (-4ab)
D (4ab)
Explanation opens after your attempt
Step 1
Concept
\(2\times2a\times(-b)=-4ab\). Exam tip: keep the negative sign with the term.
Step 2
Why this answer is correct
The correct answer is C. (-4ab). \(2\times2a\times(-b)=-4ab\). Exam tip: keep the negative sign with the term.
Step 3
Exam Tip
\(2\times2a\times(-b)=-4ab\) है। परीक्षा में ऋण चिन्ह को पद के साथ रखें।
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( (x+2y+3z)2 ) में (yz) वाला पद कौन सा होगा?
Which term containing (yz) appears in ( (x+2y+3z)2 )?
#three term square
#mixed term
#yz
A (6yz)
B (12yz)
C (5yz)
D (2yz)
Explanation opens after your attempt
Step 1
Concept
\(2\times2y\times3z=12yz\). Exam tip: in the square of three terms, take twice the product of every pair.
Step 2
Why this answer is correct
The correct answer is B. (12yz). \(2\times2y\times3z=12yz\). Exam tip: in the square of three terms, take twice the product of every pair.
Step 3
Exam Tip
\(2\times2y\times3z=12yz\) होता है। परीक्षा में तीन पदों के वर्ग में हर जोड़े का दुगुना गुणन लें।
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( (3x-2y+z)2 ) में (xy) और (yz) पदों का योग क्या है?
What is the sum of the (xy)-term and (yz)-term in ( (3x-2y+z)2 )?
#three term square
#term sum
#negative coefficients
A ( -12xy-4yz )
B ( -12xy+4yz )
C ( 6xy-4yz )
D ( -6xy-2yz )
Explanation opens after your attempt
Correct Answer
A. ( -12xy-4yz )
Step 1
Concept
The (xy)-term is (2\cdot3x\cdot(-2y)=-12xy) and the (yz)-term is (2\cdot(-2y)\cdot z=-4yz). Their sum is (-12xy-4yz).
Step 2
Why this answer is correct
The correct answer is A. ( -12xy-4yz ). The (xy)-term is (2\cdot3x\cdot(-2y)=-12xy) and the (yz)-term is (2\cdot(-2y)\cdot z=-4yz). Their sum is (-12xy-4yz).
Step 3
Exam Tip
(xy) पद (2\cdot3x\cdot(-2y)=-12xy) और (yz) पद (2\cdot(-2y)\cdot z=-4yz) है। दोनों का योग (-12xy-4yz) है।
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( (x+2y+z)2 -\(x^2+4y^2+z^2\) ) का सरल रूप क्या है?
What is the simplified form of ( (x+2y+z)2 -\(x^2+4y^2+z^2\) )?
#three term square
#simplification
#pair products
A (4xy+2xz+4yz)
B (2xy+2xz+2yz)
C (4xy+4xz+2yz)
D (2xy+4xz+4yz)
Explanation opens after your attempt
Correct Answer
A. (4xy+2xz+4yz)
Step 1
Concept
After subtracting square terms, only twice the pair products remain. They are (4xy), (2xz), and (4yz).
Step 2
Why this answer is correct
The correct answer is A. (4xy+2xz+4yz). After subtracting square terms, only twice the pair products remain. They are (4xy), (2xz), and (4yz).
Step 3
Exam Tip
वर्ग पद घटाने पर केवल जोड़ीदार दोगुने पद बचते हैं। ये (4xy), (2xz) और (4yz) हैं।
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( (a+b+c)2 -\(a^2+b^2+c^2+2ab\) ) का सरल रूप क्या है?
What is the simplified form of ( (a+b+c)2 -\(a^2+b^2+c^2+2ab\) )?
#three term square
#partial subtraction
#pair terms
A (2bc+2ca)
B (2ab+2bc)
C (2ca)
D (2bc)
Explanation opens after your attempt
Correct Answer
A. (2bc+2ca)
Step 1
Concept
In the three-term square, (2ab+2bc+2ca) appear. After subtracting the given (2ab), (2bc+2ca) remains.
Step 2
Why this answer is correct
The correct answer is A. (2bc+2ca). In the three-term square, (2ab+2bc+2ca) appear. After subtracting the given (2ab), (2bc+2ca) remains.
Step 3
Exam Tip
तीन पदों के वर्ग में (2ab+2bc+2ca) आते हैं। दिए गए (2ab) को घटाने पर (2bc+2ca) बचता है।
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( (3a-2b+c)2 ) में (bc) वाला पद कौन सा है?
Which is the (bc)-term in ( (3a-2b+c)2 )?
#three term square
#bc term
#negative sign
A (2bc)
B (-4bc)
C (-2bc)
D (4bc)
Explanation opens after your attempt
Step 1
Concept
Twice the product of (-2b) and (c) is (2\cdot(-2b)\cdot c=-4bc). Match both sign and coefficient carefully.
Step 2
Why this answer is correct
The correct answer is C. (-2bc). Twice the product of (-2b) and (c) is (2\cdot(-2b)\cdot c=-4bc). Match both sign and coefficient carefully.
Step 3
Exam Tip
(-2b) और (c) का दोगुना गुणनफल (-4bc) नहीं बल्कि (2\cdot(-2b)\cdot c=-4bc) है। सही विकल्प में चिन्ह और गुणांक मिलाएँ।
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