Choose the factorisation of ( 27x^3+8y^3 ).

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.