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Which of the following expressions is a perfect cube of a binomial and can therefore be factorised using a cube identity?
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Answer and explanation
Correct answer: \(8x^3-36x^2y+54xy^2-27y^3\)
Using \((a-b)^3=a^3-3a^2b+3ab^2-b^3\), put \(a=2x\) and \(b=3y\). This gives option A, \((2x-3y)^3\). Option C has the wrong sign for the last term. Exam tip: check the first and last terms first.
Frequently asked questions
What is the correct answer to this question?
\(8x^3-36x^2y+54xy^2-27y^3\)
Why is this the correct answer?
Using \((a-b)^3=a^3-3a^2b+3ab^2-b^3\), put \(a=2x\) and \(b=3y\). This gives option A, \((2x-3y)^3\). Option C has the wrong sign for the last term. Exam tip: check the first and last terms first.
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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