Class 9 Mathematics - Exploring Algebraic Identities - Factorisation Hard Quiz

Mathematics Exploring Algebraic Identities Factorisation Hard Class 9 Level 65

Level 65 • 5/50 questions • 30 seconds per question.

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Question 1/5 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 65

\(36m^2-49n^2\) का सही गुणनखंडन क्या है?

What is the correct factorisation of \(36m^2-49n^2\)?

Explanation opens after your attempt
Correct Answer

D. ( (6m+7n)(6m-7n) )सही गुणनखंड

Step 1

Concept

This is the form ( (6m)2-(7n)2 ). Exam tip: apply the difference of squares identity.

Step 2

Why this answer is correct

The correct answer is D. ( (6m+7n)(6m-7n) ) / सही गुणनखंड. This is the form ( (6m)2-(7n)2 ). Exam tip: apply the difference of squares identity.

Step 3

Exam Tip

यह ( (6m)2-(7n)2 ) का रूप है। परीक्षा में वर्गों के अंतर की पहचान लगाएँ।

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Question 2/5 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 65

\( a^3+125b^3 \) का गुणनखंडन क्या है?

What is the factorisation of \( a^3+125b^3 \)?

Explanation opens after your attempt
Correct Answer

A. ( (a+5b)\(a^2-5ab+25b^2\) )सही रूप

Step 1

Concept

This is (a-3+(5b)3). In sum of cubes, the second factor is \(a^2-5ab+25b^2\).

Step 2

Why this answer is correct

The correct answer is A. ( (a+5b)\(a^2-5ab+25b^2\) ) / सही रूप. This is (a-3+(5b)3). In sum of cubes, the second factor is \(a^2-5ab+25b^2\).

Step 3

Exam Tip

यह (a-3+(5b)3) है। घनों के योग में दूसरा गुणनखंड \(a^2-5ab+25b^2\) होता है।

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Question 3/5 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 65

\( 64x^3-27y^3 \) का सही गुणनखंडन चुनिए।

Choose the correct factorisation of \( 64x^3-27y^3 \).

Explanation opens after your attempt
Correct Answer

B. ( (4x-3y)\(16x^2+12xy+9y^2\) )सही रूप

Step 1

Concept

This is ( (4x)3-(3y)3 ). Exam tip: in difference of cubes, all terms of the second factor are positive.

Step 2

Why this answer is correct

The correct answer is B. ( (4x-3y)\(16x^2+12xy+9y^2\) ) / सही रूप. This is ( (4x)3-(3y)3 ). Exam tip: in difference of cubes, all terms of the second factor are positive.

Step 3

Exam Tip

यह ( (4x)3-(3y)3 ) है। परीक्षा में घनों के अंतर में दूसरे गुणनखंड के सभी पद धन होते हैं।

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Question 4/5 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 65

\( 8a^3+27b^3 \) का गुणनखंडन कौन-सा है?

Which is the factorisation of \( 8a^3+27b^3 \)?

Explanation opens after your attempt
Correct Answer

A. ( (2a+3b)\(4a^2-6ab+9b^2\) )सही रूप

Step 1

Concept

This is ( (2a)3+(3b)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. ( (2a+3b)\(4a^2-6ab+9b^2\) ) / सही रूप. This is ( (2a)3+(3b)3 ). Exam tip: identify cube roots and apply the sum of cubes identity.

Step 3

Exam Tip

यह ( (2a)3+(3b)3 ) है। परीक्षा में घनमूल पहचानकर घनों के योग की पहचान लगाएँ।

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Question 5/5 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 65

\(125p^3-8q^3\) का सही गुणनखंडन क्या है?

What is the correct factorisation of \(125p^3-8q^3\)?

Explanation opens after your attempt
Correct Answer

A. ( (5p-2q)\(25p^2+10pq+4q^2\) )सही रूप

Step 1

Concept

This is ( (5p)3-(2q)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. ( (5p-2q)\(25p^2+10pq+4q^2\) ) / सही रूप. This is ( (5p)3-(2q)3 ). Exam tip: keep all terms positive in the second factor of difference of cubes.

Step 3

Exam Tip

यह ( (5p)3-(2q)3 ) है। परीक्षा में घनों के अंतर का दूसरा गुणनखंड धन पदों वाला रखें।

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