Question

Factorize each of the following expressions:
$8x^2{y}^3-x^5$

Answer 1

Given: $8x^2{y}^3-x^5$

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

$=x^2(2y-x)(4y^2+2xy+x^2)$

Hence, $8x^2{y}^3-x^5=x^2(2y-x)(4y^2+2xy+x^2).$