Question

How do you factor the expression `25x^2-64`?

Answer 1

`25x^2-64 = (5x-8)(5x+8)`

Explanation:

The difference of squares identity can be written:

`A^2-B^2=(A-B)(A+B)`

In the given example, both `25x^2 = (5x)^2` and `64 = 8^2` are perfect squares. So we can put `A=5x` and `B=8` to find:

`25x^2-64 = (5x)^2-8^2 = (5x-8)(5x+8)`