What is the factorisation of ( a^3+b^3 )?
Answer and explanation
Correct answer: \((a+b)(a^2-ab+b^2)\)
The identity for the sum of cubes is \(a^3+b^3=(a+b)(a^2-ab+b^2)\), so option A is correct. \((a-b)(a^2+ab+b^2)\) is the factorisation of the difference of cubes, \(a^3-b^3\), so option B is not correct. Exam tip: for a sum of cubes, use \(+\) in the first bracket and \(-\) for the middle term in the second bracket.
Frequently asked questions
What is the correct answer to this question?
\((a+b)(a^2-ab+b^2)\)
Why is this the correct answer?
The identity for the sum of cubes is \(a^3+b^3=(a+b)(a^2-ab+b^2)\), so option A is correct. \((a-b)(a^2+ab+b^2)\) is the factorisation of the difference of cubes, \(a^3-b^3\), so option B is not correct. Exam tip: for a sum of cubes, use \(+\) in the first bracket and \(-\) for the middle term in the second bracket.
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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