Question

Factorize each of the following expressions:
$8a^3-b^3-4ax+2bx$

Answer 1

Given: $8a^3-b^3-4ax+2bx$

$\therefore 8a^3-b^3-4ax+2bx$
$=\left[\right(2a{)}^3-b^3]-2x(2a-b)$
$=(2a-b)\left[\right(2a{)}^2+2a\times b+b^2]-2x(2a-b)$

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

$=(2a-b)\left[\right(2a{)}^2+2a\times b+b^2-2x]$

$=(2a-b)[4a^2+2ab+b^2-2x]$

Hence, $8a^3-b^3-4ax+2bx$
$=(2a-b)(4a^2+2ab+b^2-2x).$