Factorize the following expressions: 8 x^2 y^3-x^5 - Vidyadip

Question

Factorize the following expressions:
$8 x^2 y^3-x^5$

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Answer

$8 x^2 y^3-x^5$
$=x^2\left((2 y)^3-x^3\right)$
$=x^2(2 y-x)\left((2 y)^2+2 y \times x+x^2\right)$
${\left[\therefore x^3-y^3=(x-y)\left(x^2+x y+y^2\right)\right]}$
$=x^2(2 y-x)\left(4 y^2+2 x y+x^2\right)$
$\therefore 8 x^2 y^3-x^5=x^2(2 y-x)\left(4 y^2+2 x y+x^2\right)$

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