Question

Factorize: $25m^2-70mn+49n^2$.

Answer 1

Let $5m=a$ and $7n=b$,

Then,

$a^2=25m^2$ and $b^2=49n^2$

Also, $(a-b{)}^2=a^2+b^2-2ab$ {Standard identity}

$=25m^2+49m^2-2\times 5m\times 7n$

$=25m^2+49m^2-70mn$

Therefore,

$25m^2-70mn+49m^2=(5m-7n{)}^2$