differences of squares and other even powers a

Question

Differences of Squares (and other even powers) ?

A square monomial is a monomial which is the square of another monomial. Here are some examples:
25 is the square of 5
x² is the square of x
x⁴y⁶ is the square of x²y³
2⁵x⁴y⁶ is the square of 5x²y³

How do you know if a monomial is a square? It's easy. It's a square if

1. the coefficient is a perfect square (which, by the way, means it can't be negative) and

2. all the exponents on the variables are even.

Remember that the word difference means subtraction. So here's an example of a difference of squares:

25 - 4x².
(Notice that 25 is a perfect square, and so is 4x².)
Factoring a difference of squares is easy.

Step 1: Rewrite the two terms as squares of something.
25 - 4x²
= 52 - (2x)²
Step 2: Apply the rule a² - b² = (a -b )(a + b).

= (5 -2x)(5 + 2x)