Question

Factorize the following expression:

$125-8x^3-27y^3-90xy$

Answer 1

Factorizing the given expression:

$$\begin{gathered} 125-8x^3-27y^3-90xy \\ ={\left(5\right)}^3+{(-2x)}^3+{(-3y)}^3-3\times 5\times (-2x)\times (-3y) \\ =a^3+b^3+c^3-3abc,wherea=5,b=-2xandc=-3y \\ =(a+b+c)(a^2+b^2+c^2-ab-bc-ca) \\ =(5-2x-3y)(25+4x^2+9y^2+10x-6xy+15y) \end{gathered}$$

Hence, after factorization, we get, $125-8x^3-27y^3-90xy=(5-2x-3y)(25+4x^2+9y^2+10x-6xy+15y)$.