Question

How do you factor completely `25x^2 -y^4`?

Answer 1

`25x^2-y^4=(5x+y^2)(5x-y^2)`

Explanation:

As `25x^2-y^4` is difference of two squares, to factorize it we can use the identity `a^2-b^2=(a+b)(a-b)`

Hence `25x^2-y^4=(5x)^2-(y^2)^2`

= `(5x+y^2)(5x-y^2)`