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

1 Answer
May 14, 2015

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)