What type of binomial will result in a difference of squares

If you have a binomial where both terms are a perfect square, you can factor it using difference of squares.

This also works when you have a number plus another number.

I'll provide two examples:

(x^2 - 9)

The difference of squares states: (a^2 - b^2) = (a + b) (a - b)

In this case, (x^2 - 9) = (x + 3) (x - 3)

We can also apply the difference of squares with a number plus another.

(x^2 + 25)

We can rewrite this binomial as: (x^2 - (-25))

Now, we can apply the same steps to factor.

(x^2 - (-25)) = (x + (√-25)) (x - (√-25))

Because we have √-25, we can simplify it by multiplying it by i, which will remove the negative.

This leaves us with (x + 5i) (x - 5i), which is the factored form of x^2 + 25.

We can verify this by using FOIL.

x^2 - 5ix + 5ix - 25i^2

x^2 + 25i^2

i^2 can be interpreted as - 1, and so we can change the + to -

x^2 - 25