What is application of special products and factoring​

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)

proof:

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)

factoring strategies

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.