Question

How do you use the difference of two squares formula to factor `25x^6 - a44y^10`?

Answer 1

I think the formula in the question should be `25x^6 - 144y^10`.

On the assumption that I am correct, notice that:

`25x^6 - 144y^10 = (5x^3)^2 - (12y^5)^2`

The right hand side is of the form `a^2 - b^2`, so it factors as `(a+b)(a-b)` as follows:

`(5x^3)^2 - (12y^5)^2 = (5x^3 + 12y^5)(5 x^3 - 12y^5)`