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Which of the following expressions can be factorised directly using the identity for the sum of cubes, \(a^3+b^3=(a+b)(a^2-ab+b^2)\)?
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Answer and explanation
Correct answer: \(125x^3+64y^3\)
Since \(125x^3=(5x)^3\) and \(64y^3=(4y)^3\), option A is a sum of two cubes. Option B is a difference of cubes, so it needs another identity. Exam tip: first check whether both terms are perfect cubes.
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What is the correct answer to this question?
\(125x^3+64y^3\)
Why is this the correct answer?
Since \(125x^3=(5x)^3\) and \(64y^3=(4y)^3\), option A is a sum of two cubes. Option B is a difference of cubes, so it needs another identity. Exam tip: first check whether both terms are perfect 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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