Question

Factorise the following by taking out the common factors:
c) $2x^{5}y+8x^3{y}^2–12x^2{y}^3$

Answer 1

Given:
$2x^{5}y+8x^3{y}^2–12x^2{y}^3$

The common factor is $2x^{2}y$

Dividing the above expression throughout by $2x^{2}y$, We get,

$\left\{\frac{2x^{5}y}{2x^{2}y}\right\}+\left\{\frac{8x^3{y}^2}{2x^{2}y}\right\}-\left\{\frac{12x^2{y}^3}{2x^{2}y}\right\}$

$=x^3+4xy–6y^2$

$\therefore 2x^{5}y+8x^3{y}^2–12x^2{y}^3=2x^{2}y(x^3+4xy–6y^2)$.