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Factorise $a^3 - b^3$.

A$(a-b)(a^2 - ab + b^2)$
B$(a-b)(a^2 + 2ab + b^2)$
C$(a-b)(a^2 + ab + b^2)$
D$(a-b)^3$
Answer & Solution
Correct answer: C. $(a-b)(a^2 + ab + b^2)$
The difference-of-cubes identity is $a^3-b^3=(a-b)(a^2+ab+b^2)$. Thus option C is correct. Option A has the wrong sign on $ab$, and option B has the incorrect coefficient $2$ on $ab$.
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