Question

Factorize the following using the Identities:
$49m^2-56m+16$

Answer 1

$49m^2-56m+16$
In this expression, we can express $49m^2=(7m{)}^2$ and $16=4^2$
Using the Identity $a^2-2ab+b^2=(a-b{)}^2$ with $a=7m$ and $b=4$,
$49m^2-56m+16=(7m{)}^2-2(7m\left)\right(4)+4^2$
$=(7m-4{)}^2$
$\therefore$ The factors of $49m^2-56m+16$ are $(7m-4)$ and $(7m-4)$