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difference of fourth powers MCQ Questions for Class 9

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3 questions tagged with difference of fourth powers.

Question 1/3 Hard Mathematics Exploring Algebraic Identities Factorisation Class 9 Level 71

\(16a^4-81b^4\) का पूर्ण गुणनखंड रूप क्या है?

What is the complete factorised form of \(16a^4-81b^4\)?

Explanation opens after your attempt
Correct Answer

B. ( (2a-3b)(2a+3b)\(4a^2+9b^2\) )

Step 1

Concept

First write \(16a^4-81b^4\) as (\(4a^2\)2-\(9b^2\)2). Then factor \(4a^2-9b^2\) further.

Step 2

Why this answer is correct

The correct answer is B. ( (2a-3b)(2a+3b)\(4a^2+9b^2\) ). First write \(16a^4-81b^4\) as (\(4a^2\)2-\(9b^2\)2). Then factor \(4a^2-9b^2\) further.

Step 3

Exam Tip

पहले \(16a^4-81b^4\) को (\(4a^2\)2-\(9b^2\)2) लिखें। फिर \(4a^2-9b^2\) को आगे तोड़ें।

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Question 2/3 Hard Mathematics Exploring Algebraic Identities Factorisation Class 9 Level 71

\(81a^4-16b^4\) का पूर्ण गुणनखंड क्या है?

What is the complete factorisation of \(81a^4-16b^4\)?

Explanation opens after your attempt
Correct Answer

B. ( (3a-2b)(3a+2b)\(9a^2+4b^2\) )

Step 1

Concept

Here (81a-4=\(9a^2\)2) and (16b-4=\(4b^2\)2). Exam tip: factor \(9a^2-4b^2\) further too.

Step 2

Why this answer is correct

The correct answer is B. ( (3a-2b)(3a+2b)\(9a^2+4b^2\) ). Here (81a-4=\(9a^2\)2) and (16b-4=\(4b^2\)2). Exam tip: factor \(9a^2-4b^2\) further too.

Step 3

Exam Tip

(81a-4=\(9a^2\)2) और (16b-4=\(4b^2\)2) हैं। परीक्षा में \(9a^2-4b^2\) को आगे भी तोड़ें।

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Question 3/3 Hard Mathematics Exploring Algebraic Identities Factorisation Class 9 Level 71

\(a^4-b^4\) का पूर्ण गुणनखंड रूप चुनिए।

Choose the complete factorisation of \(a^4-b^4\).

Explanation opens after your attempt
Correct Answer

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

Step 1

Concept

In \(a^4-b^4\), first use difference of squares and then factor \(a^2-b^2\). Exam tip: \(a^2+b^2\) is usually not factored further here.

Step 2

Why this answer is correct

The correct answer is C. ( (a-b)(a+b)\(a^2+b^2\) ). In \(a^4-b^4\), first use difference of squares and then factor \(a^2-b^2\). Exam tip: \(a^2+b^2\) is usually not factored further here.

Step 3

Exam Tip

\(a^4-b^4\) में पहले अंतर वर्ग और फिर \(a^2-b^2\) का गुणनखंडन करें। परीक्षा में \(a^2+b^2\) को सामान्यतः आगे नहीं तोड़ा जाता।

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