A perfect square is a quadratic expression that factors into two identical binomials.
For example, if you multiply (FOIL) these two identical binomials factors:
(x + 2)(x + 2)
You get this quadratic expression:
x2 + 4x + 4
And, turning things around, if you factor this quadratic expression:
x2 + 4x + 4
You get these two identical binomial factors:
(x + 2)(x + 2)
Therefore, the quadratic expression x2 + 4x + 4 is a perfect square since it factors into two identical binomials which are (x+ 2) and (x+ 2).
Notice that (x + 2)(x + 2) can be written (x + 2)2. So:
x2 + 4x + 4
equals
(x + 2)2
Here are some more examples of perfect squares:
x2 + 10x + 25 = (x + 5)(x + 5) = (x + 5)2
x2 - 6x + 9 = (x - 3)(x - 3) = (x - 3)2