Question

How do you factor `7x^2y^2-63y^4` ?

Answer 1

`7x^2y^2-63y^4 = 7y^2(x-3y)(x+3y)`

Explanation:

The difference of squares identity can be written:

`a^2-b^2 = (a-b)(a+b)`

We will use this with `a=x^2` and `b=(3y)^2`, but first separate out the common factor `7y^2`...

`7x^2y^2-63y^4 = 7y^2(x^2-9y^2)`

`color(white)(7x^2y^2-63y^4) = 7y^2(x^2-(3y)^2)`

`color(white)(7x^2y^2-63y^4) = 7y^2(x-3y)(x+3y)`