Question

Factorize each of the following expressions:
$64a^3-b^3$

Answer 1

Given: $64a^3-b^3$

$\therefore 64a^3-b^3$
$=(4a{)}^3-(b{)}^3$
$=(4a-b)\left[\right(4a{)}^2+4a\times b+\left(b{)}^2\right]$

$[\therefore x^3-y^3=(x-y\left)\right(x^2+xy+y^2\left)\right]$

$=(4a-b)(16a^2+4ab+b^2)$

Hence, $64a^3-b^3=(4a-b)(16a^2+4ab+b^2)$.