Choose the factorisation of ( 27x^3+8y^3 ).
Answer and explanation
Correct answer: \((3x+2y)(9x^2-6xy+4y^2)\)
Since \(27x^3+8y^3=(3x)^3+(2y)^3\), use \(a^3+b^3=(a+b)(a^2-ab+b^2)\). Substituting \(a=3x\) and \(b=2y\) gives \((3x+2y)(9x^2-6xy+4y^2)\). Option B uses the signs for the difference-of-cubes identity, so it represents \(27x^3-8y^3\), not the given expression. Exam tip: for a sum of cubes, the middle term in the second factor is negative.
Frequently asked questions
What is the correct answer to this question?
\((3x+2y)(9x^2-6xy+4y^2)\)
Why is this the correct answer?
Since \(27x^3+8y^3=(3x)^3+(2y)^3\), use \(a^3+b^3=(a+b)(a^2-ab+b^2)\). Substituting \(a=3x\) and \(b=2y\) gives \((3x+2y)(9x^2-6xy+4y^2)\). Option B uses the signs for the difference-of-cubes identity, so it represents \(27x^3-8y^3\), not the given expression. Exam tip: for a sum of cubes, the middle term in the second factor is negative.
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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