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. 27x3 - 75xy2     (you can factor out 3x)
= 3x (9x2 - 25y2)    (this is the difference of two squares)
= 3x ((3x)2 - (5y)2)
= 3x (3x - 5y) (3x + 5y)

3. a (x + 2)2 - ay2     (you can factor out an a)
= a [(x + 2)2 - y2]    (this is the difference of two squares)
= a [((x+2) - y) ((x + 2) + y)]
= a (x + 2 - y) (x + 2 + y)

4. x2 - 36    (difference of two squares)
= (x)2 - (6)2
= (x + 6) (x - 6)

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