Question

Factorize each of the following expressions:
$32a^3+108b^3$

Answer 1

Given: $32a^3+108b^3$

$\therefore 32a^3+108b^3$
$=4(8a^3+27b^3)$
$=4\left[\right(2a{)}^3+\left(3b{)}^3\right]$
$=4\left[\right(2a+3b\left)\right((2a{)}^2-2a\times 3b+(3b{)}^2\left)\right]$

$[\therefore a^3+b^3=(a+b\left)\right(a^2-ab+b^2\left)\right]$

$=4(2a+3b)(4a^2-6ab+9b^2)$

Hence, $32a^3+108b^3=4(2a+3b)(4a^2-6ab+9b^2)$.