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 $a^3 - b^3 = (a-b)(a^2 + ab + b^2)$ (note the **plus** sign on $ab$).
Option B has the wrong sign — that's the *sum*-of-cubes companion identity $a^3 + b^3 = (a+b)(a^2 - ab + b^2)$.
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