Question

Use the difference of two squares formula to factor. Be sure to factor out any common factors.

4x^2 - 25

Answer 1

(2^2)*(x^2)-(5^2) -> Taking out the exponent, (2x-5)^2. Someone check the math.

Answer 2

Look at (x + 2)(x - 2). FOIL gives x^2 - 2x + 2x - 4.
So (x + 2)(x - 2) = x^2 - 4.

In general (x + y)(x - y) = x^2 - y^2.
This is called the "difference of squares formula" for some reason.
It makes you think you have to memorize it by rote
but it's much easier to understand it than to memorize it
since there are several other factorization "formulas" that look similar.

Answer 3

Oh and 4x^2 and 25 are both squares, so
4x^2 – 25 is a difference of two squares.

4x^2 = (2x)^2 and 25 = 5^2.

So 4x^2 – 25 = (2x + 5)(2x – 5).

If you understand the idea behind the “formula”, then
these problems will be easy for you.
Otherwise, each problem seems like its own challenge.

Answer 4

Thanks for checking that up, I forgot to do the + side of the root.