Class 9 Mathematics - Exploring Algebraic Identities - Factorisation Expert Quiz

Mathematics Exploring Algebraic Identities Factorisation Expert Class 9 Level 64

Level 64 • 7/50 questions • 25 seconds per question.

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Question 1/7 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

\(16x^2-40xy+25y^2\) किसका पूर्ण वर्ग है?

\(16x^2-40xy+25y^2\) is the perfect square of what?

Explanation opens after your attempt
Correct Answer

D. ( (4x-5y)2 )सही पूर्ण वर्ग

Step 1

Concept

This is ( (4x)2-2\cdot4x\cdot5y+(5y)2 ). Exam tip: identify a minus square from the negative middle term.

Step 2

Why this answer is correct

The correct answer is D. ( (4x-5y)2 ) / सही पूर्ण वर्ग. This is ( (4x)2-2\cdot4x\cdot5y+(5y)2 ). Exam tip: identify a minus square from the negative middle term.

Step 3

Exam Tip

यह ( (4x)2-2\cdot4x\cdot5y+(5y)2 ) है। परीक्षा में ऋण मध्य पद से घटाव वाला वर्ग पहचानें।

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Question 2/7 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

\(81a^2-49b^2\) का सही गुणनखंडन क्या है?

What is the correct factorisation of \(81a^2-49b^2\)?

Explanation opens after your attempt
Correct Answer

A. ( (9a+7b)(9a-7b) )सही रूप

Step 1

Concept

This is ( (9a)2-(7b)2 ). Exam tip: take both square roots correctly in difference of squares.

Step 2

Why this answer is correct

The correct answer is A. ( (9a+7b)(9a-7b) ) / सही रूप. This is ( (9a)2-(7b)2 ). Exam tip: take both square roots correctly in difference of squares.

Step 3

Exam Tip

यह ( (9a)2-(7b)2 ) है। परीक्षा में वर्गों के अंतर में दोनों वर्गमूल सही लें।

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Question 3/7 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

\( a^3+216b^3 \) का गुणनखंडन क्या है?

What is the factorisation of \(a^3+216b^3\)?

Explanation opens after your attempt
Correct Answer

C. ( (a+6b)\(a^2-6ab+36b^2\) )सही रूप

Step 1

Concept

This is (a-3+(6b)3). In sum of cubes, the second factor is \(a^2-6ab+36b^2\).

Step 2

Why this answer is correct

The correct answer is C. ( (a+6b)\(a^2-6ab+36b^2\) ) / सही रूप. This is (a-3+(6b)3). In sum of cubes, the second factor is \(a^2-6ab+36b^2\).

Step 3

Exam Tip

यह (a-3+(6b)3) है। घनों के योग में दूसरा गुणनखंड \(a^2-6ab+36b^2\) होता है।

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Question 4/7 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

\( 27p^3-64q^3 \) का सही गुणनखंडन चुनिए।

Choose the correct factorisation of \(27p^3-64q^3\).

Explanation opens after your attempt
Correct Answer

D. ( (3p-4q)\(9p^2+12pq+16q^2\) )सही रूप

Step 1

Concept

This is ( (3p)3-(4q)3 ). Exam tip: keep all terms positive in the second factor of difference of cubes.

Step 2

Why this answer is correct

The correct answer is D. ( (3p-4q)\(9p^2+12pq+16q^2\) ) / सही रूप. This is ( (3p)3-(4q)3 ). Exam tip: keep all terms positive in the second factor of difference of cubes.

Step 3

Exam Tip

यह ( (3p)3-(4q)3 ) है। परीक्षा में घनों के अंतर का दूसरा गुणनखंड धन पदों वाला रखें।

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Question 5/7 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

\( 27a^3+64b^3 \) का गुणनखंडन कौन-सा है?

Which is the factorisation of \(27a^3+64b^3\)?

Explanation opens after your attempt
Correct Answer

A. ( (3a+4b)\(9a^2-12ab+16b^2\) )सही रूप

Step 1

Concept

This is ( (3a)3+(4b)3 ). Exam tip: identify cube roots and apply the sum of cubes identity.

Step 2

Why this answer is correct

The correct answer is A. ( (3a+4b)\(9a^2-12ab+16b^2\) ) / सही रूप. This is ( (3a)3+(4b)3 ). Exam tip: identify cube roots and apply the sum of cubes identity.

Step 3

Exam Tip

यह ( (3a)3+(4b)3 ) है। परीक्षा में घनमूल पहचानकर घनों के योग की पहचान लगाएँ।

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Question 6/7 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

\(216p^3-125q^3\) का सही गुणनखंडन क्या है?

What is the correct factorisation of \(216p^3-125q^3\)?

Explanation opens after your attempt
Correct Answer

A. ( (6p-5q)\(36p^2+30pq+25q^2\) )सही रूप

Step 1

Concept

This is ( (6p)3-(5q)3 ). Exam tip: keep all terms positive in the second factor of difference of cubes.

Step 2

Why this answer is correct

The correct answer is A. ( (6p-5q)\(36p^2+30pq+25q^2\) ) / सही रूप. This is ( (6p)3-(5q)3 ). Exam tip: keep all terms positive in the second factor of difference of cubes.

Step 3

Exam Tip

यह ( (6p)3-(5q)3 ) है। परीक्षा में घनों के अंतर का दूसरा गुणनखंड धन पदों वाला रखें।

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Question 7/7 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

\(125x^3+216y^3\) का सही गुणनखंडन क्या है?

What is the correct factorisation of \(125x^3+216y^3\)?

Explanation opens after your attempt
Correct Answer

B. ( (5x+6y)\(25x^2-30xy+36y^2\) )सही रूप

Step 1

Concept

This is ( (5x)3+(6y)3 ). In sum of cubes, the second factor has the form \(a^2-ab+b^2\).

Step 2

Why this answer is correct

The correct answer is B. ( (5x+6y)\(25x^2-30xy+36y^2\) ) / सही रूप. This is ( (5x)3+(6y)3 ). In sum of cubes, the second factor has the form \(a^2-ab+b^2\).

Step 3

Exam Tip

यह ( (5x)3+(6y)3 ) है। घनों के योग में दूसरा गुणनखंड \(a^2-ab+b^2\) रूप का होता है।

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