special products and factoring strategies
review of three special products
recall the three special products:
difference of squares
x2 - y2 = (x - y) (x + y)
square of sum
x2 + 2xy + y2 = (x + y)2
square of difference
x2 - 2xy + y2 = (x - y)2
special products involving cubes
just as there is a difference of squares formula, there is also a difference of cubes formula.
x3 - y3 = (x - y) (x2 + xy + y2)
we use the distributive law on the right hand side
x (x2 + xy + y2) - y (x2 + xy + y2)
= x3 + x2y + xy2 - x2y - xy2 - y3
now combine like terms to get
x3 - y3
next, we state the sum of cubes formula.
x3 + y3 = (x + y)(x2 - xy + y2)
always pull out the gcf first
look for special products. if there are only two terms then look for sum of cubes or difference of squares or cubes. if there are three terms, look for squares of a difference or a sum.
if there are three terms and the first coefficient is 1 then use simple trinomial factoring.
if there are three terms and the first coefficient is not 1 then use the ac method.
if there are four terms then try factoring by grouping.