Question

Factorize the following using the Identities:
$9x^{2}y-4y^3$

Answer 1

$9x^{2}y-4y^3=y[9x^2-4y^2]$
$-y\left[\right(3x{)}^2-\left(2y{)}^2\right]$
Comparing $(3x{)}^2-(2y{)}^2$ with $a^2-b^2$, we see that $a=3x$ and $b=2y$
Using $a^2-b^2=(a+b)(a-b)$, where, $a=3x,b=2y$,
$9x^{2}y-4y^3=y\left[\right(3x+2y\left)\right(3x-2y\left)\right]$