Question

Factorise the following:
x³ $-$ 27y³ + 125 + 45xy

Answer 1

$$\begin{gathered} x^3-27y^3+125+45xy \\ ={\left(x\right)}^3+{\left(-3y\right)}^3+{\left(5\right)}^3-3\times \left(x\right)\left(-3y\right)\left(5\right) \\ =\left[x+\left(-3y\right)+5\right]\left[x^2+{\left(-3y\right)}^2+5^2-x\times \left(-3y\right)-\left(-3y\right)\times 5-5\times x\right] \\ =\left(x-3y+5\right)\left(x^2+9y^2+25+3xy+15y-5x\right) \end{gathered}$$