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Which of the following expressions can be factorised as the difference of two perfect cubes?
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Answer and explanation
Correct answer: \(x^3-27\)
\(x^3-27=x^3-3^3\), so it is a difference of two perfect cubes. Using \(a^3-b^3=(a-b)(a^2+ab+b^2)\), it factorises as \((x-3)(x^2+3x+9)\). In contrast, \(x^3+27\) is a sum of cubes. Exam tip: recognise \(27=3^3\).
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What is the correct answer to this question?
\(x^3-27\)
Why is this the correct answer?
\(x^3-27=x^3-3^3\), so it is a difference of two perfect cubes. Using \(a^3-b^3=(a-b)(a^2+ab+b^2)\), it factorises as \((x-3)(x^2+3x+9)\). In contrast, \(x^3+27\) is a sum of cubes. Exam tip: recognise \(27=3^3\).
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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