What is a perfect square?

A perfect squareis a quadratic expression that factors into two identical binomials.

For example, if you multiply these binomials:

(x+ 2)(x+ 2)

You get:

x²+ 4x+ 4

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 = (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

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