Class 9 Mathematics - Exploring Algebraic Identities - Factorisation Hard Quiz

Mathematics Exploring Algebraic Identities Factorisation Hard Class 9 Level 63

Level 63 • 8/50 questions • 30 seconds per question.

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Question 1/8 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

\(9x^2-24xy+16y^2\) का सही रूप कौन-सा है?

Which is the correct form of \(9x^2-24xy+16y^2\)?

Explanation opens after your attempt
Correct Answer

B. ( (3x-4y)2 )सही पूर्ण वर्ग

Step 1

Concept

This is ( (3x)2-2\cdot3x\cdot4y+(4y)2 ). Exam tip: identify the sign of the middle term.

Step 2

Why this answer is correct

The correct answer is B. ( (3x-4y)2 ) / सही पूर्ण वर्ग. This is ( (3x)2-2\cdot3x\cdot4y+(4y)2 ). Exam tip: identify the sign of the middle term.

Step 3

Exam Tip

यह ( (3x)2-2\cdot3x\cdot4y+(4y)2 ) है। परीक्षा में मध्य पद का चिह्न पहचानें।

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Question 2/8 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

\(25p^2-36q^2\) का गुणनखंडन क्या है?

What is the factorisation of \(25p^2-36q^2\)?

Explanation opens after your attempt
Correct Answer

C. ( (5p+6q)(5p-6q) )सही रूप

Step 1

Concept

This is the form ( (5p)2-(6q)2 ). Exam tip: take the square roots of both squares correctly.

Step 2

Why this answer is correct

The correct answer is C. ( (5p+6q)(5p-6q) ) / सही रूप. This is the form ( (5p)2-(6q)2 ). Exam tip: take the square roots of both squares correctly.

Step 3

Exam Tip

यह ( (5p)2-(6q)2 ) का रूप है। परीक्षा में दोनों वर्गों के वर्गमूल सही लें।

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Question 3/8 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

\(16a^2-40ab+25b^2\) का गुणनखंडन कौन-सा है?

Which is the factorisation of \(16a^2-40ab+25b^2\)?

Explanation opens after your attempt
Correct Answer

B. ( (4a-5b)2 )सही पूर्ण वर्ग

Step 1

Concept

This is ( (4a)2-2\cdot4a\cdot5b+(5b)2 ). Exam tip: identify the minus square from the negative middle term.

Step 2

Why this answer is correct

The correct answer is B. ( (4a-5b)2 ) / सही पूर्ण वर्ग. This is ( (4a)2-2\cdot4a\cdot5b+(5b)2 ). Exam tip: identify the minus square from the negative middle term.

Step 3

Exam Tip

यह ( (4a)2-2\cdot4a\cdot5b+(5b)2 ) है। परीक्षा में ऋण मध्य पद से घटाव वर्ग पहचानें।

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Question 4/8 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

\( a^3+b^3 \) का गुणनखंडन क्या है?

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

Explanation opens after your attempt
Correct Answer

A. ( (a+b)\(a^2-ab+b^2\) )सही रूप

Step 1

Concept

In sum of cubes, the second factor is \(a^2-ab+b^2\). Exam tip: keep the middle sign negative.

Step 2

Why this answer is correct

The correct answer is A. ( (a+b)\(a^2-ab+b^2\) ) / सही रूप. In sum of cubes, the second factor is \(a^2-ab+b^2\). Exam tip: keep the middle sign negative.

Step 3

Exam Tip

घनों के योग में दूसरा गुणनखंड \(a^2-ab+b^2\) होता है। परीक्षा में बीच का चिह्न ऋण रखें।

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Question 5/8 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

\( a^3-b^3 \) किसके बराबर है?

What is \( a^3-b^3 \) equal to?

Explanation opens after your attempt
Correct Answer

A. ( (a-b)\(a^2+ab+b^2\) )सही गुणनखंड

Step 1

Concept

In difference of cubes, ( (a-b)\(a^2+ab+b^2\) ) appears. Exam tip: keep cube and square identities separate.

Step 2

Why this answer is correct

The correct answer is A. ( (a-b)\(a^2+ab+b^2\) ) / सही गुणनखंड. In difference of cubes, ( (a-b)\(a^2+ab+b^2\) ) appears. Exam tip: keep cube and square identities separate.

Step 3

Exam Tip

घनों के अंतर में ( (a-b)\(a^2+ab+b^2\) ) आता है। परीक्षा में घन और वर्ग पहचान अलग रखें।

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Question 6/8 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

\( 27x^3+8y^3 \) का गुणनखंडन चुनिए।

Choose the factorisation of \( 27x^3+8y^3 \).

Explanation opens after your attempt
Correct Answer

A. ( (3x+2y)\(9x^2-6xy+4y^2\) )सही रूप

Step 1

Concept

This is ( (3x)3+(2y)3 ). Exam tip: identify cube roots (3x) and (2y).

Step 2

Why this answer is correct

The correct answer is A. ( (3x+2y)\(9x^2-6xy+4y^2\) ) / सही रूप. This is ( (3x)3+(2y)3 ). Exam tip: identify cube roots (3x) and (2y).

Step 3

Exam Tip

यह ( (3x)3+(2y)3 ) है। परीक्षा में घनमूल (3x) और (2y) पहचानें।

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Question 7/8 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

\( 64m^3-125n^3 \) का सही गुणनखंडन क्या है?

What is the correct factorisation of \( 64m^3-125n^3 \)?

Explanation opens after your attempt
Correct Answer

A. ( (4m-5n)\(16m^2+20mn+25n^2\) )सही रूप

Step 1

Concept

This is ( (4m)3-(5n)3 ). Exam tip: in difference of cubes, the second factor has all positive terms.

Step 2

Why this answer is correct

The correct answer is A. ( (4m-5n)\(16m^2+20mn+25n^2\) ) / सही रूप. This is ( (4m)3-(5n)3 ). Exam tip: in difference of cubes, the second factor has all positive terms.

Step 3

Exam Tip

यह ( (4m)3-(5n)3 ) है। परीक्षा में घनों के अंतर का दूसरा गुणनखंड सभी धन पदों वाला होता है।

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Question 8/8 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

\(8x^3+27\) का सही गुणनखंडन कौन-सा है?

Which is the correct factorisation of \(8x^3+27\)?

Explanation opens after your attempt
Correct Answer

A. ( (2x+3)\(4x^2-6x+9\) )सही रूप

Step 1

Concept

This is ( (2x)3+33 ), so the sum of cubes identity applies. Exam tip: identify cube roots first.

Step 2

Why this answer is correct

The correct answer is A. ( (2x+3)\(4x^2-6x+9\) ) / सही रूप. This is ( (2x)3+33 ), so the sum of cubes identity applies. Exam tip: identify cube roots first.

Step 3

Exam Tip

यह ( (2x)3+33 ) है, इसलिए घनों के योग की पहचान लगती है। परीक्षा में घनमूल पहले पहचानें।

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