Question

How do you factor `(x^2+8)^2-36x^2`?

Answer 1

`(x^2+6x +8)(x^2-6x+8)`

Explanation:

As you can see, you have the difference of two squares: `(x^2+8)^2` is obviously the square of `(x^2+8)`, and `36x^2` is the square of `6x`.

A known formula states that the difference of squares is

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

So, we have that

`(x^2+8)^2-36x^2 = (x^2+8 +6x)(x^2+8-6x)`