A * perfect square* is a

For example, if you multiply (FOIL) these
two * identical binomials factors*:

(x + 2)(x + 2)

You get this ** quadratic expression**:

x^{2} + 4x + 4

And, turning things around, if you factor this ** quadratic
expression**:

x^{2} + 4x + 4

You get these two ** identical binomial factors**:

(x + 2)(x + 2)

Therefore, the quadratic expression x^{2} + 4x + 4 is a perfect square since it factors into two identical binomials which are (* x*+ 2) and (

Notice that (x + 2)(x + 2) can be written (x + 2)^{2}. So:

x^{2} + 4x + 4

equals

(x + 2)^{2}

Here are some more examples of perfect squares:

x^{2} + 10x + 25 = (x + 5)(x + 5) = (x + 5)^{2}

x^{2} - 6x + 9 = (x - 3)(x - 3) = (x - 3)^{2}