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Which of the following expressions can be factorised by applying the standard identity for the difference of squares twice in succession?
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Answer and explanation
Correct answer: \(a^4-b^4\)
\(a^4-b^4=(a^2-b^2)(a^2+b^2)\), and then \(a^2-b^2=(a-b)(a+b)\). Thus, the difference-of-squares identity is used twice. \(a^4+b^4\) has a plus sign, so this identity does not apply directly. Exam tip: first identify perfect-square terms.
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What is the correct answer to this question?
\(a^4-b^4\)
Why is this the correct answer?
\(a^4-b^4=(a^2-b^2)(a^2+b^2)\), and then \(a^2-b^2=(a-b)(a+b)\). Thus, the difference-of-squares identity is used twice. \(a^4+b^4\) has a plus sign, so this identity does not apply directly. Exam tip: first identify perfect-square terms.
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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