1. Factoring the Difference of Squares
The difference of squares.
2 2
a - b = (a -b) (a + b)
2
a - 9, for example, factors to (a - 3)(a + 3).
2. Factoring the Square of a Binomial
Learn to recognize polynomials that are squares of binomials:
2 2 2
a + 2ab + b = (a + b)
2 2 2
a - 2ab + b = (a -b)
2 2
For example, 4x + 12x + 9 factors to (2x + 3)
2 2
n - 10n + 25 factors to (n -5).
3 . Simplifying an Algebraic Fraction
Simplifying an algebraic fraction is a similar to simplifying a numerical fraction: cancel out common factors in numerator and denominator.
2
a + 7a + 12
____________
2
a - 9
2
a + 7a + 12 = (a + 3) (a + 4)
2
a - 9 = (a + 3) (a - 3)
Thus, we can cancel out the identical expressions (a + 3) in the numerator and denominator, leaving us with (a + 4) /(a - 3).