Question

Use the formula to find the factors.

(1) x³ − 8y³

Answer 1

x³ − 8y³ can be factorised as:

$$\begin{gathered} x^3-8y^3 \\ ={\left(x\right)}^3-{\left(2y\right)}^3 \\ =\left(x-2y\right)\left[x^2+x\times 2y+{\left(2y\right)}^2\right]\left[\mathrm{using}\mathrm{the}\mathrm{formula}{a}^3-b^3=\left(a-b\right)\left(a^2+ab+b^2\right)\right] \\ =\left(x-2y\right)\left(x^2+2xy+4y^2\right) \end{gathered}$$