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Which of the following expressions can be factorised using the identity for the difference of cubes?
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Answer and explanation
Correct answer: \(27a^3-8b^3\)
Since \(27a^3=(3a)^3\) and \(8b^3=(2b)^3\), the expression has the form \(A^3-B^3\). Thus it factors as \((3a-2b)(9a^2+6ab+4b^2)\). Exam tip: first identify perfect cubes; \(m^2-16\) is a difference of squares, not cubes.
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What is the correct answer to this question?
\(27a^3-8b^3\)
Why is this the correct answer?
Since \(27a^3=(3a)^3\) and \(8b^3=(2b)^3\), the expression has the form \(A^3-B^3\). Thus it factors as \((3a-2b)(9a^2+6ab+4b^2)\). Exam tip: first identify perfect cubes; \(m^2-16\) is a difference of squares, not cubes.
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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