Factorize a^3-b^3 (O Level Math Tuition Question)

(a-b)^3=a^3-3a^2b+3ab^2-b^3

So,
\begin{array}{rcl}  a^3-b^3&=&(a-b)^3+3a^2b-3ab^2\\  &=&(a-b)(a-b)^2+3a^2b-3ab^2\\  &=&(a-b)(a^2-2ab+b^2)+(a-b)(3ab)\\  &=&(a-b)(a^2+ab+b^2)  \end{array}

Author: mathtuition88

http://mathtuition88.com

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