Question

Factorize:
125 − 8x³ − 27y³ − 90xy

Answer 1

$$\begin{gathered} 125-8x^3-27y^3-90xy=5^3+{\left(-2x\right)}^3+{\left(-3y\right)}^3-3\times 5\times \left(-2x\right)\times \left(-3y\right) \\ =\left[5+\left(-2x\right)+\left(-3y\right)\right]\left[5^2+{\left(-2x\right)}^2+{\left(-3y\right)}^2-5\times \left(-2x\right)-\left(-2x\right)\left(-3y\right)-5\times \left(-3y\right)\right] \\ =\left(5-2x-3y\right)\left(25+4x^2+9y^2+10x-6xy+15y\right) \end{gathered}$$