Question

Use the formula to find the factors.

(4) (x + y)³ − 125

Answer 1

(x + y)³ − 125 can be factorised as:

$$\begin{gathered} {\left(x-y\right)}^3-125 \\ ={\left(x+y\right)}^3-{\left(5\right)}^3 \\ =\left[\left(x+y\right)-5\right]\left[{\left(x+y\right)}^2+\left(x+y\right)\times 5+5^2\right]\left[\mathrm{using}\mathrm{the}\mathrm{formula}{a}^3-b^3=\left(a-b\right)\left(a^2+ab+b^2\right)\right] \\ =\left(x+y-5\right)\left(x^2+y^2+2xy+5x+5y+25\right) \end{gathered}$$