Factorise 8m³ + 27n³.

Correct answer: (2m + 3n)(4m² − 6mn + 9n²)

The correct answer is A: (2m + 3n)(4m² − 6mn + 9n²). Recognise each term as a cube: 8m³ = (2m)³ and 27n³ = (3n)³. Apply u³ + v³ = (u + v)(u² − uv + v²), with u = 2m and v = 3n. The first factor is 2m + 3n. In the second factor, u² = 4m², −uv = −(2m)(3n) = −6mn, and v² = 9n². Thus the result is option A. Option B uses the difference-of-cubes pattern and has the wrong first sign. Option C does not use the correct cube roots and therefore has incorrect coefficients. Option D has a positive 6mn term; multiplying it would create additional positive mixed terms rather than the cancellation required for a sum of cubes. Memory cue: sum of cubes has + in the first factor and − between the squared and mixed terms in the second factor.