Question

factorize 5y^2- 125z^2​

Answer 1

Answer:

$5\left(y+5z\right)\left(y-5z\right)$

Step-by-step explanation:

$\mathrm{The \;given \;equation \;is \; 5y^2-125z^2}$

$\mathrm{Factor\:out\:common\:term\:}5:\quad 5\left(y^2-25z^2\right)\\\\= 5\left(y^2-25z^2\right)$

$\left y^2-25z^2\right$
$25z^2 = \left(5z\right)^2$
==> $\left y^2-25z^2\right = y^2-\left(5z\right)^2$

$\mathrm{Apply\:Difference\:of\:Two\:Squares\:Formula:\:}x^2-y^2=\left(x+y\right)\left(x-y\right)$
$y^2-\left(5z\right)^2=\left(y+5z\right)\left(y-5z\right)$

So the factored expression is
$5\left(y+5z\right)\left(y-5z\right)$