Class 9 Mathematics - Exploring Algebraic Identities - Factorisation Hard Quiz

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\( 121a^2-49b^2 \) का सही गुणनखंड रूप कौन सा है?

Which is the correct factor form of \( 121a^2-49b^2 \)?

Explanation opens after your attempt
Correct Answer

A. ( (11a+7b)(11a-7b) )

Step 1

Concept

This is ( (11a)2-(7b)2 ). For difference of squares, use (a-2-b-2=(a+b)(a-b)).

Step 2

Why this answer is correct

The correct answer is A. ( (11a+7b)(11a-7b) ). This is ( (11a)2-(7b)2 ). For difference of squares, use (a-2-b-2=(a+b)(a-b)).

Step 3

Exam Tip

यह ( (11a)2-(7b)2 ) है। अंतर के वर्गों में (a-2-b-2=(a+b)(a-b)) लगता है।

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( (2x+5)2-4x-2 ) का गुणनखंड रूप क्या है?

What is the factor form of ( (2x+5)2-4x-2 )?

Explanation opens after your attempt
Correct Answer

A. (5(4x+5))

Step 1

Concept

This is ( (2x+5)2-(2x)2 ). The factors simplify to (5(4x+5)).

Step 2

Why this answer is correct

The correct answer is A. (5(4x+5)). This is ( (2x+5)2-(2x)2 ). The factors simplify to (5(4x+5)).

Step 3

Exam Tip

यह ( (2x+5)2-(2x)2 ) है। गुणनखंड (5(4x+5)) बनते हैं।

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\( x^2+2xy+y^2-25 \) का गुणनखंड रूप क्या है?

What is the factor form of \( x^2+2xy+y^2-25 \)?

Explanation opens after your attempt
Correct Answer

A. ( (x+y+5)(x+y-5) )

Step 1

Concept

First identify (x-2+2xy+y-2=(x+y)2). Then apply difference of squares to ( (x+y)2-52 ).

Step 2

Why this answer is correct

The correct answer is A. ( (x+y+5)(x+y-5) ). First identify (x-2+2xy+y-2=(x+y)2). Then apply difference of squares to ( (x+y)2-52 ).

Step 3

Exam Tip

पहले (x-2+2xy+y-2=(x+y)2) पहचानें। फिर ( (x+y)2-52 ) पर अंतर के वर्ग लगाएँ।

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\( 4p^2-12pq+9q^2-16 \) का गुणनखंड रूप क्या है?

What is the factor form of \( 4p^2-12pq+9q^2-16 \)?

Explanation opens after your attempt
Correct Answer

A. ( (2p-3q+4)(2p-3q-4) )

Step 1

Concept

First (4p-2-12pq+9q-2=(2p-3q)2). Then factor ( (2p-3q)2-42 ).

Step 2

Why this answer is correct

The correct answer is A. ( (2p-3q+4)(2p-3q-4) ). First (4p-2-12pq+9q-2=(2p-3q)2). Then factor ( (2p-3q)2-42 ).

Step 3

Exam Tip

पहले (4p-2-12pq+9q-2=(2p-3q)2) है। फिर ( (2p-3q)2-42 ) का गुणनखंड करें।

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\( x^2+6x+9-y^2 \) का सही गुणनखंड रूप कौन सा है?

Which is the correct factor form of \( x^2+6x+9-y^2 \)?

Explanation opens after your attempt
Correct Answer

C. ( (x+3+y)(x+3-y) )

Step 1

Concept

First identify (x-2+6x+9=(x+3)2). Then apply the difference of squares identity to ( (x+3)2-y-2 ).

Step 2

Why this answer is correct

The correct answer is C. ( (x+3+y)(x+3-y) ). First identify (x-2+6x+9=(x+3)2). Then apply the difference of squares identity to ( (x+3)2-y-2 ).

Step 3

Exam Tip

पहले (x-2+6x+9=(x+3)2) पहचानें। फिर ( (x+3)2-y-2 ) पर अंतर के वर्गों की सर्वसमिका लगाएँ।

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