Question

Factorize 5y^2- 125z^2​

Answer 1

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

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)`