A student has factorised \(8p^3+q^3\) as \((2p+q)(4p^2-2pq+q^2)\). Which statement about the solution is correct?

Correct answer: The factorisation is correct; it is based on the identity \(a^3+b^3=(a+b)(a^2-ab+b^2)\).

Here, \(8p^3=(2p)^3\) and \(q^3=q^3\). Applying the sum-of-cubes identity gives the stated factorisation. Exam tip: in \(a^3+b^3\), the middle term of the second factor has a negative sign.