Unit 6  Objective 2  Factoring: Common Factors and
Difference of Squares
You should always try to factor out any common monomial
factor and then you try to factor the rest of the problem.
Examples:
1. 
4x + 4y
(You can factor out a 4)
= 4 (x + y)


2. 
27x^{3}  75xy^{2}
(you can factor out 3x)
= 3x (9x^{2}  25y^{2}) (this
is the difference of two squares)
= 3x ((3x)^{2}  (5y)^{2})
= 3x (3x  5y) (3x + 5y)


3. 
a (x + 2)^{2}  ay^{2}
(you can factor out an a)
= a [(x + 2)^{2}  y^{2}] (this
is the difference of two squares)
= a [((x+2)  y) ((x + 2) + y)]
= a (x + 2  y) (x + 2 + y)


4. 
x^{2}  36 (difference of two squares)
= (x)^{2}  (6)^{2}
= (x + 6) (x  6) 

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