Difference of squares

Some binomials can be written as the difference of two squares. In order to factor a difference of two

squares, it's important to recognize some perfect squares. The first 25 perfect squares are as follows:

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576 and 625.

The formula for factoring the difference of two squares is

(x^2 - y^2) = (x - y)(x + y)

It's easy to think of this as just taking √x^2 and √y^2, which is x and y. Both binomials in the factored form will have x and y, one with a “-” between them and one with a “+” between them.

Example: Factor x^2 – 16.

Notice that x^2 and 16 are both perfect squares

.

√x^2 = x and √16 = 4, therefore the factored form of x^2 – 16 is (x - 4)(x + 4).

Example: Factor 4x^2 – 25.

√4x^2 = 2x and √25 = 5, therefore the factored form of 4x^2 - 25 is (2x - 5)(2x + 5).

Example: Factor 25y^2 - 49x^2.

√25y^2 = 5y and √49x^2 = 7x, therefore the factored form of 25y^2 - 49x^2 is (5y - 7x)(5y + 7x).

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