## Tuesday, August 11, 2009

### GMAT - FACTORING ALGEBRAIC EXPRESSIONS

`1. Factoring the Difference of SquaresThe difference of squares. 2      2a   -  b   = (a -b) (a + b) 2a  -  9, for example,  factors to (a  - 3)(a + 3).2. Factoring the Square of a BinomialLearn to recognize polynomials that are squares of binomials: 2         2         2a + 2ab + b = (a + b) 2         2        2a - 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 FractionSimplifying an algebraic fraction is a similar to simplifying a numerical fraction: cancel out common factors in numerator and denominator.  2                a + 7a + 12   ____________ 2a -  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).`