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Which of the following expressions is a factor of \(a^4-b^4\)?
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Answer and explanation
Correct answer: \(a^2+b^2\)
Write \(a^4-b^4\) as a difference of squares: \((a^2)^2-(b^2)^2=(a^2-b^2)(a^2+b^2)\). Hence \(a^2+b^2\) is a factor. Exam tip: for fourth powers, first check whether they can be treated as squares.
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What is the correct answer to this question?
\(a^2+b^2\)
Why is this the correct answer?
Write \(a^4-b^4\) as a difference of squares: \((a^2)^2-(b^2)^2=(a^2-b^2)(a^2+b^2)\). Hence \(a^2+b^2\) is a factor. Exam tip: for fourth powers, first check whether they can be treated as squares.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Exploring Algebraic Identities. Topic: Algebraic identities.
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