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Which of the following is the correct factorised form of the difference of two cubes, \(a^3-b^3\)?
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Answer and explanation
Correct answer: \((a-b)(a^2+ab+b^2)\)
\(a^3-b^3=(a-b)(a^2+ab+b^2)\). On expansion, the middle terms cancel, leaving \(a^3-b^3\). Option B has the wrong sign in the middle term. Exam tip: for a difference, the first factor is always \(a-b\).
Frequently asked questions
What is the correct answer to this question?
\((a-b)(a^2+ab+b^2)\)
Why is this the correct answer?
\(a^3-b^3=(a-b)(a^2+ab+b^2)\). On expansion, the middle terms cancel, leaving \(a^3-b^3\). Option B has the wrong sign in the middle term. Exam tip: for a difference, the first factor is always \(a-b\).
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Exploring Algebraic Identities. Topic: Factorisation.
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