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cube expansion MCQ Questions for Class 9

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14 questions tagged with cube expansion.

Question 1/14 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

( (x+2)3-\(x^3+8\) ) का सरल रूप क्या है?

What is the simplified form of ( (x+2)3-\(x^3+8\) )?

Explanation opens after your attempt
Correct Answer

A. (6x(x+2))सही रूप

Step 1

Concept

( (x+2)3=x-3+6x-2+12x+8 ). The middle terms form (6x(x+2)).

Step 2

Why this answer is correct

The correct answer is A. (6x(x+2)) / सही रूप. ( (x+2)3=x-3+6x-2+12x+8 ). The middle terms form (6x(x+2)).

Step 3

Exam Tip

( (x+2)3=x-3+6x-2+12x+8 ) है। बीच के पद (6x(x+2)) बनाते हैं।

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Question 2/14 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

( (x-4)3 ) का सही विस्तार कौन-सा है?

Which is the correct expansion of ( (x-4)3 )?

Explanation opens after your attempt
Correct Answer

A. \(x^3-12x^2+48x-64\)सही विस्तार

Step 1

Concept

In the cube of a difference, signs follow (+), (-), (+), (-). Exam tip: check both \(4^2\) and \(4^3\).

Step 2

Why this answer is correct

The correct answer is A. \(x^3-12x^2+48x-64\) / सही विस्तार. In the cube of a difference, signs follow (+), (-), (+), (-). Exam tip: check both \(4^2\) and \(4^3\).

Step 3

Exam Tip

घटाव के घन में चिह्न (+), (-), (+), (-) क्रम में आते हैं। परीक्षा में \(4^2\) और \(4^3\) दोनों देखें।

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Question 3/14 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

( (2x+5y)3 ) में \(xy^2\) का गुणांक क्या होगा?

What is the coefficient of \(xy^2\) in ( (2x+5y)3 )?

Explanation opens after your attempt
Correct Answer

A. (150)सही गुणांक

Step 1

Concept

(3(2x)(5y)2=150xy-2). Exam tip: square the second term completely.

Step 2

Why this answer is correct

The correct answer is A. (150) / सही गुणांक. (3(2x)(5y)2=150xy-2). Exam tip: square the second term completely.

Step 3

Exam Tip

(3(2x)(5y)2=150xy-2) है। परीक्षा में दूसरे पद का वर्ग पूरा करें।

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Question 4/14 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

( (a+b)3-\(a^3+b^3\) ) का गुणनखंड रूप क्या है?

What is the factor form of ( (a+b)3-\(a^3+b^3\) )?

Explanation opens after your attempt
Correct Answer

A. (3ab(a+b))सही रूप

Step 1

Concept

The middle terms in the cube expansion are \(3a^2b+3ab^2\). They are written as (3ab(a+b)).

Step 2

Why this answer is correct

The correct answer is A. (3ab(a+b)) / सही रूप. The middle terms in the cube expansion are \(3a^2b+3ab^2\). They are written as (3ab(a+b)).

Step 3

Exam Tip

घन विस्तार के मध्य पद \(3a^2b+3ab^2\) हैं। इन्हें (3ab(a+b)) के रूप में लिखा जाता है।

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Question 5/14 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

( (3x+2y)3 ) में \(x^2y\) का गुणांक क्या होगा?

What is the coefficient of \(x^2y\) in ( (3x+2y)3 )?

Explanation opens after your attempt
Correct Answer

B. (54)सही गुणांक

Step 1

Concept

(3(3x)2(2y)=54x-2y). Exam tip: square the complete term (3x).

Step 2

Why this answer is correct

The correct answer is B. (54) / सही गुणांक. (3(3x)2(2y)=54x-2y). Exam tip: square the complete term (3x).

Step 3

Exam Tip

(3(3x)2(2y)=54x-2y) है। परीक्षा में पूरे (3x) का वर्ग करें।

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Question 6/14 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

( (x+4)3-(x-4)3 ) में \(x^2\) वाला पद क्या होगा?

What will be the term containing \(x^2\) in ( (x+4)3-(x-4)3 )?

Explanation opens after your attempt
Correct Answer

B. \(24x^2\)

Step 1

Concept

The difference gives \(6x^2\cdot4=24x^2\). Exam tip: identify the \(x^2\) term quickly in cube differences.

Step 2

Why this answer is correct

The correct answer is B. \(24x^2\). The difference gives \(6x^2\cdot4=24x^2\). Exam tip: identify the \(x^2\) term quickly in cube differences.

Step 3

Exam Tip

अंतर में \(6x^2\cdot4=24x^2\) मिलता है। परीक्षा में घन अंतर में \(x^2\) वाला पद जल्दी पहचानें।

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Question 7/14 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 65

( (x+1)3-\(x^3+1\) ) का सरल रूप क्या है?

What is the simplified form of ( (x+1)3-\(x^3+1\) )?

Explanation opens after your attempt
Correct Answer

A. (3x(x+1))सही रूप

Step 1

Concept

( (x+1)3=x-3+3x-2+3x+1 ). The middle terms form (3x(x+1)).

Step 2

Why this answer is correct

The correct answer is A. (3x(x+1)) / सही रूप. ( (x+1)3=x-3+3x-2+3x+1 ). The middle terms form (3x(x+1)).

Step 3

Exam Tip

( (x+1)3=x-3+3x-2+3x+1 ) है। बीच के पद (3x(x+1)) बनाते हैं।

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Question 8/14 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 65

( (x-3)3 ) का सही विस्तार कौन-सा है?

Which is the correct expansion of ( (x-3)3 )?

Explanation opens after your attempt
Correct Answer

A. \(x^3-9x^2+27x-27\)सही विस्तार

Step 1

Concept

In the cube of a difference, signs occur in (+), (-), (+), (-) order. Exam tip: check both \(3^2\) and \(3^3\).

Step 2

Why this answer is correct

The correct answer is A. \(x^3-9x^2+27x-27\) / सही विस्तार. In the cube of a difference, signs occur in (+), (-), (+), (-) order. Exam tip: check both \(3^2\) and \(3^3\).

Step 3

Exam Tip

घटाव के घन में चिह्न (+), (-), (+), (-) क्रम में आते हैं। परीक्षा में \(3^2\) और \(3^3\) दोनों देखें।

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Question 9/14 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 65

( (5x+2y)3 ) में \(x y^2\) का गुणांक क्या होगा?

What is the coefficient of \(xy^2\) in ( (5x+2y)3 )?

Explanation opens after your attempt
Correct Answer

B. (60)सही गुणांक

Step 1

Concept

(3(5x)(2y)2=60xy-2). Exam tip: square the second term completely.

Step 2

Why this answer is correct

The correct answer is B. (60) / सही गुणांक. (3(5x)(2y)2=60xy-2). Exam tip: square the second term completely.

Step 3

Exam Tip

(3(5x)(2y)2=60xy-2) है। परीक्षा में दूसरे पद का वर्ग पूरा करें।

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Question 10/14 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 65

( (a+b)3-\(a^3+b^3\) ) को गुणनखंड रूप में कैसे लिखा जाएगा?

How will ( (a+b)3-\(a^3+b^3\) ) be written in factor form?

Explanation opens after your attempt
Correct Answer

A. (3ab(a+b))सही रूप

Step 1

Concept

The middle terms \(3a^2b+3ab^2\) form (3ab(a+b)). Exam tip: take the common factor.

Step 2

Why this answer is correct

The correct answer is A. (3ab(a+b)) / सही रूप. The middle terms \(3a^2b+3ab^2\) form (3ab(a+b)). Exam tip: take the common factor.

Step 3

Exam Tip

घन विस्तार के मध्य पद \(3a^2b+3ab^2\) मिलकर (3ab(a+b)) बनाते हैं। परीक्षा में सामान्य गुणनखंड निकालें।

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Question 11/14 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 65

( (2x+y)3 ) में \(x^2y\) का गुणांक क्या होगा?

What is the coefficient of \(x^2y\) in ( (2x+y)3 )?

Explanation opens after your attempt
Correct Answer

B. (12)सही गुणांक

Step 1

Concept

(3(2x)2y=12x-2y). Exam tip: square the whole term (2x).

Step 2

Why this answer is correct

The correct answer is B. (12) / सही गुणांक. (3(2x)2y=12x-2y). Exam tip: square the whole term (2x).

Step 3

Exam Tip

(3(2x)2y=12x-2y) है। परीक्षा में (2x) का पूरा वर्ग करें।

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Question 12/14 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

( (2a+b)3 ) में \(a^2b\) का गुणांक क्या होगा?

What is the coefficient of \(a^2b\) in ( (2a+b)3 )?

Explanation opens after your attempt
Correct Answer

A. (6)सही गुणांक

Step 1

Concept

(3(2a)2b=12a-2b), so the coefficient is (12). Exam tip: square ((2a)2) correctly.

Step 2

Why this answer is correct

The correct answer is A. (6) / सही गुणांक. (3(2a)2b=12a-2b), so the coefficient is (12). Exam tip: square ((2a)2) correctly.

Step 3

Exam Tip

(3(2a)2b=12a-2b) है, इसलिए गुणांक (12) होगा। परीक्षा में ((2a)2) को सही वर्ग करें।

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Question 13/14 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

( (a+b)3-\(a^3+b^3\) ) का सरल रूप क्या है?

What is the simplified form of ( (a+b)3-\(a^3+b^3\) )?

Explanation opens after your attempt
Correct Answer

A. (3ab(a+b))सही रूप

Step 1

Concept

( (a+b)3=a-3+3a-2b+3ab-2+b-3 ). The two middle terms form (3ab(a+b)).

Step 2

Why this answer is correct

The correct answer is A. (3ab(a+b)) / सही रूप. ( (a+b)3=a-3+3a-2b+3ab-2+b-3 ). The two middle terms form (3ab(a+b)).

Step 3

Exam Tip

( (a+b)3=a-3+3a-2b+3ab-2+b-3 ) है। बीच के दो पद (3ab(a+b)) बनाते हैं।

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Question 14/14 Hard Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

( (x+2)3 ) का विस्तार क्या है?

What is the expansion of ( (x+2)3 )?

Explanation opens after your attempt
Correct Answer

A. \(x^3+6x^2+12x+8\)सही विस्तार

Step 1

Concept

( (x+2)3=x-3+3x-2\cdot2+3x\cdot4+8 ). Exam tip: keep both terms with coefficient (3).

Step 2

Why this answer is correct

The correct answer is A. \(x^3+6x^2+12x+8\) / सही विस्तार. ( (x+2)3=x-3+3x-2\cdot2+3x\cdot4+8 ). Exam tip: keep both terms with coefficient (3).

Step 3

Exam Tip

( (x+2)3=x-3+3x-2\cdot2+3x\cdot4+8 ) है। परीक्षा में (3ab) वाले दोनों पद रखें।

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