Class 9 Mathematics - Exploring Algebraic Identities - Factorisation Hard Quiz

Mathematics Exploring Algebraic Identities Factorisation Hard Class 9 Level 69

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Question 1/50 Hard Mathematics Exploring Algebraic Identities Factorisation Class 9 Level 69

(ax+ay+bx+by) का समूह बनाकर गुणनखंडन कौन सा है?

What is the factorisation of (ax+ay+bx+by) by grouping?

Explanation opens after your attempt
Correct Answer

A. ((a+b)(x+y))

Step 1

Concept

First write (a(x+y)+b(x+y)). Then take common ((x+y)) to get ((a+b)(x+y)).

Step 2

Why this answer is correct

The correct answer is A. ((a+b)(x+y)). First write (a(x+y)+b(x+y)). Then take common ((x+y)) to get ((a+b)(x+y)).

Step 3

Exam Tip

पहले (a(x+y)+b(x+y)) लिखें। फिर समान ((x+y)) निकालकर ((a+b)(x+y)) मिलता है।

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Question 2/50 Hard Mathematics Exploring Algebraic Identities Factorisation Class 9 Level 69

(px-py+qx-qy) में सही गुणनखंड कौन से हैं?

What are the correct factors of (px-py+qx-qy)?

Explanation opens after your attempt
Correct Answer

B. ((p+q)(x-y))

Step 1

Concept

Grouping gives (p(x-y)+q(x-y)). Taking common ((x-y)) gives ((p+q)(x-y)).

Step 2

Why this answer is correct

The correct answer is B. ((p+q)(x-y)). Grouping gives (p(x-y)+q(x-y)). Taking common ((x-y)) gives ((p+q)(x-y)).

Step 3

Exam Tip

समूह बनाने पर (p(x-y)+q(x-y)) मिलता है। इसलिए समान ((x-y)) निकालकर ((p+q)(x-y)) मिलेगा।

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Question 3/50 Hard Mathematics Exploring Algebraic Identities Factorisation Class 9 Level 69

\(3a^2-12b^2\) का पूर्ण गुणनखंडन क्या है?

What is the complete factorisation of \(3a^2-12b^2\)?

Explanation opens after your attempt
Correct Answer

C. (3(a-2b)(a+2b))

Step 1

Concept

First take (3) common and split \(a^2-4b^2\) by difference of squares. Exam tip: check further factorisation after taking common factor.

Step 2

Why this answer is correct

The correct answer is C. (3(a-2b)(a+2b)). First take (3) common and split \(a^2-4b^2\) by difference of squares. Exam tip: check further factorisation after taking common factor.

Step 3

Exam Tip

पहले (3) समान निकालें और \(a^2-4b^2\) को वर्गों के अंतर से तोड़ें। परीक्षा में समान गुणनखंड निकालने के बाद भी आगे जांचें।

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Question 4/50 Hard Mathematics Exploring Algebraic Identities Factorisation Class 9 Level 69

\(x^2+10x+25-y^2\) का सही गुणनखंडन कौन सा है?

Which is the correct factorisation of \(x^2+10x+25-y^2\)?

Explanation opens after your attempt
Correct Answer

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

Step 1

Concept

First identify (x-2+10x+25=(x+5)2). Then difference of squares gives ((x+5-y)(x+5+y)).

Step 2

Why this answer is correct

The correct answer is D. ((x+5-y)(x+5+y)). First identify (x-2+10x+25=(x+5)2). Then difference of squares gives ((x+5-y)(x+5+y)).

Step 3

Exam Tip

पहले (x-2+10x+25=(x+5)2) पहचानें। फिर वर्गों के अंतर से ((x+5-y)(x+5+y)) मिलेगा।

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Question 5/50 Hard Mathematics Exploring Algebraic Identities Factorisation Class 9 Level 69

\(4x^2-20xy+25y^2\) किसका पूर्ण वर्ग है?

\(4x^2-20xy+25y^2\) is the perfect square of what?

Explanation opens after your attempt
Correct Answer

A. ((2x-5y)2)

Step 1

Concept

(4x-2=(2x)2) and (25y-2=(5y)2). The middle term is negative so ((2x-5y)2) is correct.

Step 2

Why this answer is correct

The correct answer is A. ((2x-5y)2). (4x-2=(2x)2) and (25y-2=(5y)2). The middle term is negative so ((2x-5y)2) is correct.

Step 3

Exam Tip

(4x-2=(2x)2) और (25y-2=(5y)2) है। मध्य पद ऋण है इसलिए ((2x-5y)2) सही है।

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Question 6/50 Hard Mathematics Exploring Algebraic Identities Factorisation Class 9 Level 69

\(9a^2-16b^2+6a-8b\) में कौन सा गुणनखंडन सही है?

Which factorisation is correct for \(9a^2-16b^2+6a-8b\)?

Explanation opens after your attempt
Correct Answer

B. ((3a-4b)(3a+4b+2))

Step 1

Concept

By grouping write ((3a-4b)(3a+4b)+2(3a-4b)). Take common ((3a-4b)).

Step 2

Why this answer is correct

The correct answer is B. ((3a-4b)(3a+4b+2)). By grouping write ((3a-4b)(3a+4b)+2(3a-4b)). Take common ((3a-4b)).

Step 3

Exam Tip

समूह बनाकर ((3a-4b)(3a+4b)+2(3a-4b)) लिख सकते हैं। समान ((3a-4b)) निकालें।

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Question 7/50 Hard Mathematics Exploring Algebraic Identities Factorisation Class 9 Level 69

\(x^2+7x+10\) और \(x^2+5x+6\) के गुणनखंडों में कौन सा सामान्य गुणनखंड है?

Which common factor is present in the factorisations of \(x^2+7x+10\) and \(x^2+5x+6\)?

Explanation opens after your attempt
Correct Answer

C. (x+2)

Step 1

Concept

The first is ((x+5)(x+2)) and the second is ((x+2)(x+3)). So the common factor is ((x+2)).

Step 2

Why this answer is correct

The correct answer is C. (x+2). The first is ((x+5)(x+2)) and the second is ((x+2)(x+3)). So the common factor is ((x+2)).

Step 3

Exam Tip

पहला ((x+5)(x+2)) और दूसरा ((x+2)(x+3)) है। इसलिए सामान्य गुणनखंड ((x+2)) है।

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Question 8/50 Hard Mathematics Exploring Algebraic Identities Factorisation Class 9 Level 69

\(2x^2+11x+15\) का गुणनखंडन कौन सा है?

Which is the factorisation of \(2x^2+11x+15\)?

Explanation opens after your attempt
Correct Answer

C. ((2x+3)(x+5))

Step 1

Concept

Check multiplication carefully: ((2x+5)(x+3)=2x-2+11x+15). So the correct factorisation is ((2x+5)(x+3)).

Step 2

Why this answer is correct

The correct answer is C. ((2x+3)(x+5)). Check multiplication carefully: ((2x+5)(x+3)=2x-2+11x+15). So the correct factorisation is ((2x+5)(x+3)).

Step 3

Exam Tip

((2x+5)(x+3)) से \(2x^2+11x+15\) नहीं बल्कि \(2x^2+11x+15\) ही मिलता है? गुणा जांचें और सही विकल्प ((2x+5)(x+3)) है।

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Question 9/50 Hard Mathematics Exploring Algebraic Identities Factorisation Class 9 Level 69

\(3x^2+10x+8\) के सही गुणनखंड कौन से हैं?

What are the correct factors of \(3x^2+10x+8\)?

Explanation opens after your attempt
Correct Answer

A. ((3x+4)(x+2))

Step 1

Concept

((3x+4)(x+2)=3x-2+6x+4x+8). The middle term becomes (10x).

Step 2

Why this answer is correct

The correct answer is A. ((3x+4)(x+2)). ((3x+4)(x+2)=3x-2+6x+4x+8). The middle term becomes (10x).

Step 3

Exam Tip

((3x+4)(x+2)=3x-2+6x+4x+8) है। मध्य पद (10x) बनता है।

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Question 10/50 Hard Mathematics Exploring Algebraic Identities Factorisation Class 9 Level 69

\(6x^2+13x+6\) का गुणनखंडन चुनिए।

Choose the factorisation of \(6x^2+13x+6\).

Explanation opens after your attempt
Correct Answer

B. ((2x+3)(3x+2))

Step 1

Concept

Expanding ((2x+3)(3x+2)) gives \(6x^2+4x+9x+6\). The middle term is (13x).

Step 2

Why this answer is correct

The correct answer is B. ((2x+3)(3x+2)). Expanding ((2x+3)(3x+2)) gives \(6x^2+4x+9x+6\). The middle term is (13x).

Step 3

Exam Tip

((2x+3)(3x+2)) फैलाने पर \(6x^2+4x+9x+6\) मिलता है। मध्य पद (13x) है।

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Question 11/50 Hard Mathematics Exploring Algebraic Identities Factorisation Class 9 Level 69

\(12x^2-27y^2\) का पूर्ण गुणनखंडन क्या है?

What is the complete factorisation of \(12x^2-27y^2\)?

Explanation opens after your attempt
Correct Answer

A. (3(2x-3y)(2x+3y))

Step 1

Concept

First take (3) common and split \(4x^2-9y^2\) by difference of squares. Exam tip: fully factorise the final answer.

Step 2

Why this answer is correct

The correct answer is A. (3(2x-3y)(2x+3y)). First take (3) common and split \(4x^2-9y^2\) by difference of squares. Exam tip: fully factorise the final answer.

Step 3

Exam Tip

पहले (3) समान निकालें और \(4x^2-9y^2\) को वर्गों के अंतर से तोड़ें। परीक्षा में अंतिम उत्तर को पूर्ण गुणनखंडित करें।

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Question 12/50 Hard Mathematics Exploring Algebraic Identities Factorisation Class 9 Level 69

\(a^4-b^4\) का पूर्ण गुणनखंडन कौन सा है?

Which is the complete factorisation of \(a^4-b^4\)?

Explanation opens after your attempt
Correct Answer

B. ((a-b)(a+b)\(a^2+b^2\))

Step 1

Concept

First write (a-4-b-4=\(a^2-b^2\)\(a^2+b^2\)). Then split (a-2-b-2=(a-b)(a+b)) too.

Step 2

Why this answer is correct

The correct answer is B. ((a-b)(a+b)\(a^2+b^2\)). First write (a-4-b-4=\(a^2-b^2\)\(a^2+b^2\)). Then split (a-2-b-2=(a-b)(a+b)) too.

Step 3

Exam Tip

पहले (a-4-b-4=\(a^2-b^2\)\(a^2+b^2\)) करें। फिर (a-2-b-2=(a-b)(a+b)) भी तोड़ें।

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Question 13/50 Hard Mathematics Exploring Algebraic Identities Factorisation Class 9 Level 69

\(x^4-81\) का पूर्ण गुणनखंडन क्या होगा?

What will be the complete factorisation of \(x^4-81\)?

Explanation opens after your attempt
Correct Answer

C. ((x-3)(x+3)\(x^2+9\))

Step 1

Concept

(x-4-81=\(x^2-9\)\(x^2+9\)) and (x-2-9=(x-3)(x+3)). Exam tip: check difference of squares repeatedly.

Step 2

Why this answer is correct

The correct answer is C. ((x-3)(x+3)\(x^2+9\)). (x-4-81=\(x^2-9\)\(x^2+9\)) and (x-2-9=(x-3)(x+3)). Exam tip: check difference of squares repeatedly.

Step 3

Exam Tip

(x-4-81=\(x^2-9\)\(x^2+9\)) और (x-2-9=(x-3)(x+3)) है। परीक्षा में बार बार वर्गों के अंतर को जांचें।

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Question 14/50 Hard Mathematics Exploring Algebraic Identities Factorisation Class 9 Level 69

\(x^2-2xy+y^2-25\) का सही गुणनखंडन चुनिए।

Choose the correct factorisation 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 factor ((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 factor ((x-y)2-52).

Step 3

Exam Tip

पहले (x-2-2xy+y-2=(x-y)2) पहचानें। फिर ((x-y)2-52) को तोड़ें।

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Question 15/50 Hard Mathematics Exploring Algebraic Identities Factorisation Class 9 Level 69

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

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

Explanation opens after your attempt
Correct Answer

B. ((5a-4b)2)

Step 1

Concept

(25a-2=(5a)2) and (16b-2=(4b)2). The negative middle term gives ((5a-4b)2).

Step 2

Why this answer is correct

The correct answer is B. ((5a-4b)2). (25a-2=(5a)2) and (16b-2=(4b)2). The negative middle term gives ((5a-4b)2).

Step 3

Exam Tip

(25a-2=(5a)2) और (16b-2=(4b)2) है। ऋण मध्य पद से ((5a-4b)2) मिलता है।

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Question 16/50 Hard Mathematics Exploring Algebraic Identities Factorisation Class 9 Level 69

\(5x^2+16x+3\) का गुणनखंडन क्या होगा?

What will be the factorisation of \(5x^2+16x+3\)?

Explanation opens after your attempt
Correct Answer

A. ((5x+1)(x+3))

Step 1

Concept

((5x+1)(x+3)=5x-2+15x+x+3). Therefore the middle term is (16x).

Step 2

Why this answer is correct

The correct answer is A. ((5x+1)(x+3)). ((5x+1)(x+3)=5x-2+15x+x+3). Therefore the middle term is (16x).

Step 3

Exam Tip

((5x+1)(x+3)=5x-2+15x+x+3) है। इसलिए मध्य पद (16x) मिलता है।

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Question 17/50 Hard Mathematics Exploring Algebraic Identities Factorisation Class 9 Level 69

\(6x^2-x-12\) का गुणनखंडन चुनिए।

Choose the factorisation of \(6x^2-x-12\).

Explanation opens after your attempt
Correct Answer

D. ((3x-4)(2x+3))

Step 1

Concept

((3x-4)(2x+3)=6x-2+9x-8x-12). The middle term becomes (x), so signs must be checked carefully.

Step 2

Why this answer is correct

The correct answer is D. ((3x-4)(2x+3)). ((3x-4)(2x+3)=6x-2+9x-8x-12). The middle term becomes (x), so signs must be checked carefully.

Step 3

Exam Tip

((3x-4)(2x+3)=6x-2+9x-8x-12) है। मध्य पद (x) नहीं बल्कि (x) बनेगा इसलिए चिह्न जांचना जरूरी है।

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Question 18/50 Hard Mathematics Exploring Algebraic Identities Factorisation Class 9 Level 69

\(6x^2-x-12\) के लिए सही गुणनखंड वास्तव में कौन से हैं?

For \(6x^2-x-12\), what are the actually correct factors?

Explanation opens after your attempt
Correct Answer

A. ((3x+4)(2x-3))

Step 1

Concept

((3x+4)(2x-3)=6x-2-9x+8x-12=6x-2-x-12). Exam tip: expand to check signs.

Step 2

Why this answer is correct

The correct answer is A. ((3x+4)(2x-3)). ((3x+4)(2x-3)=6x-2-9x+8x-12=6x-2-x-12). Exam tip: expand to check signs.

Step 3

Exam Tip

((3x+4)(2x-3)=6x-2-9x+8x-12=6x-2-x-12) है। परीक्षा में विस्तार करके संकेत जांचें।

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Question 19/50 Hard Mathematics Exploring Algebraic Identities Factorisation Class 9 Level 69

\(x^3+3x^2+2x\) का पूर्ण गुणनखंडन क्या है?

What is the complete factorisation of \(x^3+3x^2+2x\)?

Explanation opens after your attempt
Correct Answer

B. (x(x+1)(x+2))

Step 1

Concept

First take (x) common and factor \(x^2+3x+2\) as ((x+1)(x+2)). Exam tip: factor the trinomial after common factor.

Step 2

Why this answer is correct

The correct answer is B. (x(x+1)(x+2)). First take (x) common and factor \(x^2+3x+2\) as ((x+1)(x+2)). Exam tip: factor the trinomial after common factor.

Step 3

Exam Tip

पहले (x) समान निकालें और \(x^2+3x+2\) को ((x+1)(x+2)) करें। परीक्षा में सामान्य गुणनखंड के बाद त्रिपद भी तोड़ें।

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Question 20/50 Hard Mathematics Exploring Algebraic Identities Factorisation Class 9 Level 69

\(2x^3+8x^2+8x\) का पूर्ण गुणनखंडन कौन सा है?

Which is the complete factorisation of \(2x^3+8x^2+8x\)?

Explanation opens after your attempt
Correct Answer

A. (2x(x+2)2)

Step 1

Concept

First take (2x) common. Inside (x-2+4x+4=(x+2)2).

Step 2

Why this answer is correct

The correct answer is A. (2x(x+2)2). First take (2x) common. Inside (x-2+4x+4=(x+2)2).

Step 3

Exam Tip

पहले (2x) समान निकालें। अंदर (x-2+4x+4=(x+2)2) है।

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Question 21/50 Hard Mathematics Exploring Algebraic Identities Factorisation Class 9 Level 69

\(x^3-9x\) का पूर्ण गुणनखंडन क्या है?

What is the complete factorisation of \(x^3-9x\)?

Explanation opens after your attempt
Correct Answer

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

Step 1

Concept

First take (x) common to get (x\(x^2-9\)). Then factor (x-2-9=(x-3)(x+3)).

Step 2

Why this answer is correct

The correct answer is C. (x(x-3)(x+3)). First take (x) common to get (x\(x^2-9\)). Then factor (x-2-9=(x-3)(x+3)).

Step 3

Exam Tip

पहले (x) समान निकालकर (x\(x^2-9\)) मिलता है। फिर (x-2-9=(x-3)(x+3)) करें।

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Question 22/50 Hard Mathematics Exploring Algebraic Identities Factorisation Class 9 Level 69

\(4a^2-4ab+b^2-9c^2\) का गुणनखंडन कौन सा है?

Which is the factorisation of \(4a^2-4ab+b^2-9c^2\)?

Explanation opens after your attempt
Correct Answer

A. ((2a-b-3c)(2a-b+3c))

Step 1

Concept

First identify (4a-2-4ab+b-2=(2a-b)2). Then subtract \(9c^2\) and use difference of squares.

Step 2

Why this answer is correct

The correct answer is A. ((2a-b-3c)(2a-b+3c)). First identify (4a-2-4ab+b-2=(2a-b)2). Then subtract \(9c^2\) and use difference of squares.

Step 3

Exam Tip

पहले (4a-2-4ab+b-2=(2a-b)2) पहचानें। फिर \(9c^2\) घटाकर वर्गों के अंतर से तोड़ें।

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Question 23/50 Hard Mathematics Exploring Algebraic Identities Factorisation Class 9 Level 69

\(a^2+2a+1-b^2-2bc-c^2\) को कैसे गुणनखंडित करेंगे?

How will you factorise \(a^2+2a+1-b^2-2bc-c^2\)?

Explanation opens after your attempt
Correct Answer

A. ((a+1-b-c)(a+1+b+c))

Step 1

Concept

This is ((a+1)2-(b+c)2). Difference of squares gives two factors.

Step 2

Why this answer is correct

The correct answer is A. ((a+1-b-c)(a+1+b+c)). This is ((a+1)2-(b+c)2). Difference of squares gives two factors.

Step 3

Exam Tip

यह ((a+1)2-(b+c)2) है। वर्गों के अंतर से दो गुणनखंड मिलते हैं।

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Question 24/50 Hard Mathematics Exploring Algebraic Identities Factorisation Class 9 Level 69

\(x^2+xy+3x+3y\) में समूह बनाकर सही गुणनखंडन क्या है?

What is the correct factorisation of \(x^2+xy+3x+3y\) by grouping?

Explanation opens after your attempt
Correct Answer

B. ((x+3)(x+y))

Step 1

Concept

Grouping gives (x(x+y)+3(x+y)). Taking common ((x+y)) gives ((x+3)(x+y)).

Step 2

Why this answer is correct

The correct answer is B. ((x+3)(x+y)). Grouping gives (x(x+y)+3(x+y)). Taking common ((x+y)) gives ((x+3)(x+y)).

Step 3

Exam Tip

समूह करने पर (x(x+y)+3(x+y)) मिलता है। समान ((x+y)) निकालने पर ((x+3)(x+y)) है।

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Question 25/50 Hard Mathematics Exploring Algebraic Identities Factorisation Class 9 Level 69

(ab-ac+db-dc) का गुणनखंडन कौन सा है?

Which is the factorisation of (ab-ac+db-dc)?

Explanation opens after your attempt
Correct Answer

A. ((a+d)(b-c))

Step 1

Concept

Group as (a(b-c)+d(b-c)). Taking common ((b-c)) gives ((a+d)(b-c)).

Step 2

Why this answer is correct

The correct answer is A. ((a+d)(b-c)). Group as (a(b-c)+d(b-c)). Taking common ((b-c)) gives ((a+d)(b-c)).

Step 3

Exam Tip

समूह बनाकर (a(b-c)+d(b-c)) लिखें। समान ((b-c)) निकालने पर ((a+d)(b-c)) मिलता है।

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Question 26/50 Hard Mathematics Exploring Algebraic Identities Factorisation Class 9 Level 69

\(x^2-y^2+4x+4\) का गुणनखंडन क्या होगा?

What will be the factorisation of \(x^2-y^2+4x+4\)?

Explanation opens after your attempt
Correct Answer

A. ((x+2-y)(x+2+y))

Step 1

Concept

(x-2+4x+4=(x+2)2). Therefore it becomes ((x+2)2-y-2).

Step 2

Why this answer is correct

The correct answer is A. ((x+2-y)(x+2+y)). (x-2+4x+4=(x+2)2). Therefore it becomes ((x+2)2-y-2).

Step 3

Exam Tip

(x-2+4x+4=(x+2)2) है। इसलिए यह ((x+2)2-y-2) बनता है।

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Question 27/50 Hard Mathematics Exploring Algebraic Identities Factorisation Class 9 Level 69

\(9x^2+12xy+4y^2-16\) का सही गुणनखंडन चुनिए।

Choose the correct factorisation of \(9x^2+12xy+4y^2-16\).

Explanation opens after your attempt
Correct Answer

A. ((3x+2y-4)(3x+2y+4))

Step 1

Concept

First (9x-2+12xy+4y-2=(3x+2y)2). Then subtract \(16=4^2\) and use difference of squares.

Step 2

Why this answer is correct

The correct answer is A. ((3x+2y-4)(3x+2y+4)). First (9x-2+12xy+4y-2=(3x+2y)2). Then subtract \(16=4^2\) and use difference of squares.

Step 3

Exam Tip

पहले (9x-2+12xy+4y-2=(3x+2y)2) है। फिर \(16=4^2\) घटाकर अंतर के वर्ग लगाएं।

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Question 28/50 Hard Mathematics Exploring Algebraic Identities Factorisation Class 9 Level 69

\(16p^2-24pq+9q^2-r^2\) का गुणनखंडन क्या है?

What is the factorisation of \(16p^2-24pq+9q^2-r^2\)?

Explanation opens after your attempt
Correct Answer

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

Step 1

Concept

(16p-2-24pq+9q-2=(4p-3q)2). Subtracting \(r^2\) forms a difference of squares.

Step 2

Why this answer is correct

The correct answer is A. ((4p-3q-r)(4p-3q+r)). (16p-2-24pq+9q-2=(4p-3q)2). Subtracting \(r^2\) forms a difference of squares.

Step 3

Exam Tip

(16p-2-24pq+9q-2=(4p-3q)2) है। फिर \(r^2\) घटाने पर वर्गों का अंतर बनता है।

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Question 29/50 Hard Mathematics Exploring Algebraic Identities Factorisation Class 9 Level 69

\(2x^2-5x-3\) का सही गुणनखंडन कौन सा है?

Which is the correct factorisation of \(2x^2-5x-3\)?

Explanation opens after your attempt
Correct Answer

B. ((2x+1)(x-3))

Step 1

Concept

( (2x+1)(x-3)=2x-2-6x+x-3=2x-2-5x-3). Exam tip: check the sum of opposite-sign terms.

Step 2

Why this answer is correct

The correct answer is B. ((2x+1)(x-3)). ( (2x+1)(x-3)=2x-2-6x+x-3=2x-2-5x-3). Exam tip: check the sum of opposite-sign terms.

Step 3

Exam Tip

((2x+1)(x-3)=2x-2-6x+x-3=2x-2-5x-3) है। परीक्षा में विपरीत चिह्न वाले पदों का योग जांचें।

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Question 30/50 Hard Mathematics Exploring Algebraic Identities Factorisation Class 9 Level 69

\(3x^2-14x-5\) का गुणनखंडन चुनिए।

Choose the factorisation of \(3x^2-14x-5\).

Explanation opens after your attempt
Correct Answer

A. ((3x+1)(x-5))

Step 1

Concept

((3x+1)(x-5)=3x-2-15x+x-5=3x-2-14x-5). Exam tip: confirm by expansion.

Step 2

Why this answer is correct

The correct answer is A. ((3x+1)(x-5)). ((3x+1)(x-5)=3x-2-15x+x-5=3x-2-14x-5). Exam tip: confirm by expansion.

Step 3

Exam Tip

((3x+1)(x-5)=3x-2-15x+x-5=3x-2-14x-5) है। परीक्षा में विस्तार से उत्तर पक्का करें।

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Question 31/50 Hard Mathematics Exploring Algebraic Identities Factorisation Class 9 Level 69

\(4x^2-4x-15\) के गुणनखंड कौन से हैं?

What are the factors of \(4x^2-4x-15\)?

Explanation opens after your attempt
Correct Answer

C. ((2x-5)(2x+3))

Step 1

Concept

((2x-5)(2x+3)=4x-2+6x-10x-15=4x-2-4x-15). Exam tip: check the sum of cross terms.

Step 2

Why this answer is correct

The correct answer is C. ((2x-5)(2x+3)). ((2x-5)(2x+3)=4x-2+6x-10x-15=4x-2-4x-15). Exam tip: check the sum of cross terms.

Step 3

Exam Tip

((2x-5)(2x+3)=4x-2+6x-10x-15=4x-2-4x-15) है। परीक्षा में क्रॉस पदों का योग देखें।

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Question 32/50 Hard Mathematics Exploring Algebraic Identities Factorisation Class 9 Level 69

\(15x^2+2x-8\) का सही गुणनखंडन क्या है?

What is the correct factorisation of \(15x^2+2x-8\)?

Explanation opens after your attempt
Correct Answer

D. ((3x-2)(5x+4))

Step 1

Concept

((3x-2)(5x+4)=15x-2+12x-10x-8). The middle term becomes (2x).

Step 2

Why this answer is correct

The correct answer is D. ((3x-2)(5x+4)). ((3x-2)(5x+4)=15x-2+12x-10x-8). The middle term becomes (2x).

Step 3

Exam Tip

((3x-2)(5x+4)=15x-2+12x-10x-8) है। मध्य पद (2x) बनता है।

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Question 33/50 Hard Mathematics Exploring Algebraic Identities Factorisation Class 9 Level 69

\(49m^2-70mn+25n^2\) का गुणनखंडन कौन सा है?

Which is the factorisation of \(49m^2-70mn+25n^2\)?

Explanation opens after your attempt
Correct Answer

A. ((7m-5n)2)

Step 1

Concept

(49m-2=(7m)2) and (25n-2=(5n)2). The middle term is \(-2\cdot7m\cdot5n\).

Step 2

Why this answer is correct

The correct answer is A. ((7m-5n)2). (49m-2=(7m)2) and (25n-2=(5n)2). The middle term is \(-2\cdot7m\cdot5n\).

Step 3

Exam Tip

(49m-2=(7m)2) और (25n-2=(5n)2) है। मध्य पद \(-2\cdot7m\cdot5n\) है।

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Question 34/50 Hard Mathematics Exploring Algebraic Identities Factorisation Class 9 Level 69

\(a^2+4a+4-c^2\) का गुणनखंड रूप क्या है?

What is the factor form of \(a^2+4a+4-c^2\)?

Explanation opens after your attempt
Correct Answer

B. ((a+2-c)(a+2+c))

Step 1

Concept

(a-2+4a+4=(a+2)2). Then split ((a+2)2-c-2) by difference of squares.

Step 2

Why this answer is correct

The correct answer is B. ((a+2-c)(a+2+c)). (a-2+4a+4=(a+2)2). Then split ((a+2)2-c-2) by difference of squares.

Step 3

Exam Tip

(a-2+4a+4=(a+2)2) है। फिर ((a+2)2-c-2) को वर्गों के अंतर से तोड़ें।

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Question 35/50 Hard Mathematics Exploring Algebraic Identities Factorisation Class 9 Level 69

\(x^2+2xy+y^2-4x-4y+4\) का गुणनखंडन क्या होगा?

What will be the factorisation of \(x^2+2xy+y^2-4x-4y+4\)?

Explanation opens after your attempt
Correct Answer

C. ((x+y-2)2)

Step 1

Concept

This is ((x+y)2-4(x+y)+4). Therefore it becomes ((x+y-2)2).

Step 2

Why this answer is correct

The correct answer is C. ((x+y-2)2). This is ((x+y)2-4(x+y)+4). Therefore it becomes ((x+y-2)2).

Step 3

Exam Tip

यह ((x+y)2-4(x+y)+4) है। इसलिए यह ((x+y-2)2) बनता है।

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Question 36/50 Hard Mathematics Exploring Algebraic Identities Factorisation Class 9 Level 69

\(a^2-2ab+b^2-9\) का गुणनखंडन कौन सा है?

Which is the factorisation of \(a^2-2ab+b^2-9\)?

Explanation opens after your attempt
Correct Answer

A. ((a-b-3)(a-b+3))

Step 1

Concept

First write (a-2-2ab+b-2=(a-b)2). Then subtract \(9=3^2\) to make difference of squares.

Step 2

Why this answer is correct

The correct answer is A. ((a-b-3)(a-b+3)). First write (a-2-2ab+b-2=(a-b)2). Then subtract \(9=3^2\) to make difference of squares.

Step 3

Exam Tip

पहले (a-2-2ab+b-2=(a-b)2) लिखें। फिर \(9=3^2\) घटाकर वर्गों का अंतर बनाएं।

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Question 37/50 Hard Mathematics Exploring Algebraic Identities Factorisation Class 9 Level 69

\(x^4+2x^2+1\) का पूर्ण गुणनखंडन क्या है?

What is the complete factorisation of \(x^4+2x^2+1\)?

Explanation opens after your attempt
Correct Answer

A. (\(x^2+1\)2)

Step 1

Concept

Treat \(x^2\) as one term and it is a perfect square. So (x-4+2x-2+1=\(x^2+1\)2).

Step 2

Why this answer is correct

The correct answer is A. (\(x^2+1\)2). Treat \(x^2\) as one term and it is a perfect square. So (x-4+2x-2+1=\(x^2+1\)2).

Step 3

Exam Tip

यह \(x^2\) को एक पद मानकर पूर्ण वर्ग है। इसलिए (x-4+2x-2+1=\(x^2+1\)2) है।

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Question 38/50 Hard Mathematics Exploring Algebraic Identities Factorisation Class 9 Level 69

\(16x^4-1\) का पूर्ण गुणनखंडन कौन सा है?

Which is the complete factorisation of \(16x^4-1\)?

Explanation opens after your attempt
Correct Answer

B. ((2x-1)(2x+1)\(4x^2+1\))

Step 1

Concept

(16x-4-1=\(4x^2-1\)\(4x^2+1\)). Then (4x-2-1=(2x-1)(2x+1)) also factors.

Step 2

Why this answer is correct

The correct answer is B. ((2x-1)(2x+1)\(4x^2+1\)). (16x-4-1=\(4x^2-1\)\(4x^2+1\)). Then (4x-2-1=(2x-1)(2x+1)) also factors.

Step 3

Exam Tip

(16x-4-1=\(4x^2-1\)\(4x^2+1\)) है। फिर (4x-2-1=(2x-1)(2x+1)) भी टूटता है।

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Question 39/50 Hard Mathematics Exploring Algebraic Identities Factorisation Class 9 Level 69

\(2a^2b+6ab^2+4ab\) का पूर्ण गुणनखंडन क्या है?

What is the complete factorisation of \(2a^2b+6ab^2+4ab\)?

Explanation opens after your attempt
Correct Answer

A. (2ab(a+3b+2))

Step 1

Concept

(2ab) is common in all three terms. Taking it out leaves (a+3b+2).

Step 2

Why this answer is correct

The correct answer is A. (2ab(a+3b+2)). (2ab) is common in all three terms. Taking it out leaves (a+3b+2).

Step 3

Exam Tip

तीनों पदों में (2ab) समान है। बाहर निकालने पर (a+3b+2) बचता है।

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Question 40/50 Hard Mathematics Exploring Algebraic Identities Factorisation Class 9 Level 69

\(3x^2y-12xy+12y\) का गुणनखंडन चुनिए।

Choose the factorisation of \(3x^2y-12xy+12y\).

Explanation opens after your attempt
Correct Answer

A. (3y(x-2)2)

Step 1

Concept

First take (3y) common and inside (x-2-4x+4=(x-2)2). Exam tip: identify the inner trinomial too.

Step 2

Why this answer is correct

The correct answer is A. (3y(x-2)2). First take (3y) common and inside (x-2-4x+4=(x-2)2). Exam tip: identify the inner trinomial too.

Step 3

Exam Tip

पहले (3y) समान निकालें और अंदर (x-2-4x+4=(x-2)2) है। परीक्षा में अंदर के त्रिपद को भी पहचानें।

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Question 41/50 Hard Mathematics Exploring Algebraic Identities Factorisation Class 9 Level 69

\(5x^2-45\) का पूर्ण गुणनखंडन क्या होगा?

What will be the complete factorisation of \(5x^2-45\)?

Explanation opens after your attempt
Correct Answer

B. (5(x-3)(x+3))

Step 1

Concept

First take (5) common and split \(x^2-9\) by difference of squares. Exam tip: look further after common factor.

Step 2

Why this answer is correct

The correct answer is B. (5(x-3)(x+3)). First take (5) common and split \(x^2-9\) by difference of squares. Exam tip: look further after common factor.

Step 3

Exam Tip

पहले (5) समान निकालें और \(x^2-9\) को वर्गों के अंतर से तोड़ें। परीक्षा में समान गुणनखंड के बाद आगे देखें।

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Question 42/50 Hard Mathematics Exploring Algebraic Identities Factorisation Class 9 Level 69

\(7x^2-28y^2\) का गुणनखंडन क्या है?

What is the factorisation of \(7x^2-28y^2\)?

Explanation opens after your attempt
Correct Answer

A. (7(x-2y)(x+2y))

Step 1

Concept

Taking (7) common gives \(x^2-4y^2\). This is ((x-2y)(x+2y)).

Step 2

Why this answer is correct

The correct answer is A. (7(x-2y)(x+2y)). Taking (7) common gives \(x^2-4y^2\). This is ((x-2y)(x+2y)).

Step 3

Exam Tip

(7) समान निकालने पर \(x^2-4y^2\) मिलता है। यह ((x-2y)(x+2y)) है।

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Question 43/50 Hard Mathematics Exploring Algebraic Identities Factorisation Class 9 Level 69

\(x^2-11x+30\) के गुणनखंड कौन से हैं?

What are the factors of \(x^2-11x+30\)?

Explanation opens after your attempt
Correct Answer

A. ((x-5)(x-6))

Step 1

Concept

(-5+(-6)=-11) and ((-5)(-6)=30). Exam tip: for a positive last term use same-sign factors.

Step 2

Why this answer is correct

The correct answer is A. ((x-5)(x-6)). (-5+(-6)=-11) and ((-5)(-6)=30). Exam tip: for a positive last term use same-sign factors.

Step 3

Exam Tip

(-5+(-6)=-11) और ((-5)(-6)=30) है। परीक्षा में धन अंतिम पद के लिए समान चिह्न वाले कारक देखें।

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Question 44/50 Hard Mathematics Exploring Algebraic Identities Factorisation Class 9 Level 69

\(x^2-x-20\) का सही गुणनखंडन चुनिए।

Choose the correct factorisation of \(x^2-x-20\).

Explanation opens after your attempt
Correct Answer

A. ((x-5)(x+4))

Step 1

Concept

(-5+4=-1) and \(-5\cdot4=-20\). Therefore ((x-5)(x+4)) is correct.

Step 2

Why this answer is correct

The correct answer is A. ((x-5)(x+4)). (-5+4=-1) and \(-5\cdot4=-20\). Therefore ((x-5)(x+4)) is correct.

Step 3

Exam Tip

(-5+4=-1) और \(-5\cdot4=-20\) है। इसलिए ((x-5)(x+4)) सही है।

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Question 45/50 Hard Mathematics Exploring Algebraic Identities Factorisation Class 9 Level 69

\(x^2+2x-24\) का गुणनखंडन क्या होगा?

What will be the factorisation of \(x^2+2x-24\)?

Explanation opens after your attempt
Correct Answer

A. ((x+6)(x-4))

Step 1

Concept

(6+(-4)=2) and (6\cdot(-4)=-24). Exam tip: check the sum of opposite-sign factors.

Step 2

Why this answer is correct

The correct answer is A. ((x+6)(x-4)). (6+(-4)=2) and (6\cdot(-4)=-24). Exam tip: check the sum of opposite-sign factors.

Step 3

Exam Tip

(6+(-4)=2) और (6\cdot(-4)=-24) है। परीक्षा में विपरीत चिह्न वाले कारकों का योग देखें।

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Question 46/50 Hard Mathematics Exploring Algebraic Identities Factorisation Class 9 Level 69

\(x^2-8x+15\) का गुणनखंडन कौन सा है?

Which is the factorisation of \(x^2-8x+15\)?

Explanation opens after your attempt
Correct Answer

A. ((x-3)(x-5))

Step 1

Concept

(-3+(-5)=-8) and ((-3)(-5)=15). Exam tip: two negative factors make the middle term negative.

Step 2

Why this answer is correct

The correct answer is A. ((x-3)(x-5)). (-3+(-5)=-8) and ((-3)(-5)=15). Exam tip: two negative factors make the middle term negative.

Step 3

Exam Tip

(-3+(-5)=-8) और ((-3)(-5)=15) है। परीक्षा में दोनों ऋण कारक मध्य पद ऋण बनाते हैं।

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Question 47/50 Hard Mathematics Exploring Algebraic Identities Factorisation Class 9 Level 69

\(2x^2+9x+10\) का सही गुणनखंडन क्या है?

What is the correct factorisation of \(2x^2+9x+10\)?

Explanation opens after your attempt
Correct Answer

A. ((2x+5)(x+2))

Step 1

Concept

((2x+5)(x+2)=2x-2+4x+5x+10). The middle term becomes (9x).

Step 2

Why this answer is correct

The correct answer is A. ((2x+5)(x+2)). ((2x+5)(x+2)=2x-2+4x+5x+10). The middle term becomes (9x).

Step 3

Exam Tip

((2x+5)(x+2)=2x-2+4x+5x+10) है। मध्य पद (9x) बनता है।

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Question 48/50 Hard Mathematics Exploring Algebraic Identities Factorisation Class 9 Level 69

\(8x^2+14x+3\) का गुणनखंडन चुनिए।

Choose the factorisation of \(8x^2+14x+3\).

Explanation opens after your attempt
Correct Answer

A. ((4x+1)(2x+3))

Step 1

Concept

((4x+1)(2x+3)=8x-2+12x+2x+3). Therefore the middle term is (14x).

Step 2

Why this answer is correct

The correct answer is A. ((4x+1)(2x+3)). ((4x+1)(2x+3)=8x-2+12x+2x+3). Therefore the middle term is (14x).

Step 3

Exam Tip

((4x+1)(2x+3)=8x-2+12x+2x+3) है। इसलिए मध्य पद (14x) मिलता है।

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Question 49/50 Hard Mathematics Exploring Algebraic Identities Factorisation Class 9 Level 69

\(9x^2-30x+25-4y^2\) का गुणनखंडन क्या है?

What is the factorisation of \(9x^2-30x+25-4y^2\)?

Explanation opens after your attempt
Correct Answer

A. ((3x-5-2y)(3x-5+2y))

Step 1

Concept

First identify (9x-2-30x+25=(3x-5)2). Then subtract (4y-2=(2y)2) and use difference of squares.

Step 2

Why this answer is correct

The correct answer is A. ((3x-5-2y)(3x-5+2y)). First identify (9x-2-30x+25=(3x-5)2). Then subtract (4y-2=(2y)2) and use difference of squares.

Step 3

Exam Tip

पहले (9x-2-30x+25=(3x-5)2) पहचानें। फिर (4y-2=(2y)2) घटाकर वर्गों का अंतर लगाएं।

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Question 50/50 Hard Mathematics Exploring Algebraic Identities Factorisation Class 9 Level 69

\(x^2+2x+1-y^2+4y-4\) का सही गुणनखंडन कौन सा है?

Which is the correct factorisation of \(x^2+2x+1-y^2+4y-4\)?

Explanation opens after your attempt
Correct Answer

A. ((x+1-y+2)(x+1+y-2))

Step 1

Concept

First identify (x-2+2x+1=(x+1)2) and (y-2-4y+4=(y-2)2). Then use difference of squares.

Step 2

Why this answer is correct

The correct answer is A. ((x+1-y+2)(x+1+y-2)). First identify (x-2+2x+1=(x+1)2) and (y-2-4y+4=(y-2)2). Then use difference of squares.

Step 3

Exam Tip

पहले (x-2+2x+1=(x+1)2) और (y-2-4y+4=(y-2)2) पहचानें। फिर वर्गों के अंतर का प्रयोग करें।

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