Recognizing Differences of Squares
The following polynomials are differences of squares:
X2 – 9, 4t2 – 49, a2 – 25b
Difference Of Squares
A2 – B2 = (A + B) (A – B)
Thus,
X2 – 9 = (x + 3) (x – 3).
To use this formula, we must be able to recognize when it applies. A difference of squares is an expression like the following:
A2 – B2.
How can we recognize such expressions? Look at A2 – B2 In order for a binomial to be a difference of squares:
a) There must be two expressions, both squares, such as
4x2 , 9, 25t4,1, x6, 49y8
b) The terms must have different signs.