What are the steps on how to factor the difference of squares?

let's say you have (x²-9)

we know it's a difference of squares because

A) Subtraction sign

B) the x²

so you would look for something times something that will give you an X² and a 9 with out having an X to the first power in the middle

we know X•X=X² and 3•3 = 9 we also know that a positive times a negative = a negative

so we can try to guess and check.

(x+3) (x-3)

x times x is X²

x times - 3 is - 3x

3 times x is + 3x

3 times - 3 is - 9

it should look like this now

(x²-3x+3x-9)

we can clean it up by subtracting + 3x by - 3x which will get rid of the x¹ that we don't want appearing in the middle.

FINAL Answer

(x+3) (x-3)

is the difference of squares for (x²-9)

The formula for the difference of squares: a^2 - b^2 = (a + b) (a - b)

Example: If x^2 - 4

x^2 - 2^2

(x + 2) (x - 2)