Question

Use the formula to find the factors.

(6) 512x³ − 343y³

Answer 1

512x³ − 343y³ can be factorised as:

$$\begin{gathered} 512x^3-343y^3 \\ ={\left(8x\right)}^3-{\left(7y\right)}^3 \\ =\left(8x-7y\right)\left[{\left(8x\right)}^2+8x\times 7y+{\left(7y\right)}^2\right]\left[\mathrm{using}\mathrm{the}\mathrm{formula}{a}^3-b^3=\left(a-b\right)\left(a^2+ab+b^2\right)\right] \\ =\left(8x-7y\right)\left(64x^2+56xy+49y^2\right) \end{gathered}$$