1. Special Case Factoring
CCM2 11-7

2. Special Case Theorems Remember the Special Case Theorems
Difference of Squares: (ax + b) (ax – b) = a2x2 – b2
Perfect Squares: (ax + b)2= a2x2 + 2abx + b2
We will use these theorems in reverse to help us factor
As in all factoring, always check for a GCF before using these methods.

3. Difference in Squares Factoring
Recognizing
Quadratic Binomial
Positive Leading Coefficient
No Linear Term
Negative Constant
Theorem
a2x2 – b2 = (ax + b) (ax – b)
Example
Factor 49x2 – 9
Square root the first term
Square root the constant
Combine the results with “+” and “-”

4. You Try: Factor the following:
25x2 - 4
81x2 - 49
4x2 - 36
(5x + 2)(5x – 2)
(9x + 7)(9x - 7)
4(x + 3)(x - 3)

5. Perfect Squares Factoring
Recognizing
Quadratic Trinomial
or the factors of ac are the same.
Even if you do not recognize a perfect square, the other methods also work.
Example
Factor 4x2 +12x + 9
Note that
So, , which is b
Using the theorem:
Perfect Squares Factoring Theorem

6. You Try: Factor the following:
x2 + 6x + 9
4x2 - 4x + 1
9x2 + 24x + 16
(x + 3)2
(2x – 1)2
(3x + 4)2

7. Summary Thank You Factoring a Difference of Squares
Factoring a Perfect Square
Thank You