1. Factoring - Difference of Squares and Perfect Square Trinomial Patterns

2. What numbers are Perfect Squares?1 4 9 16 25 36 49 64 81
100

3. Factoring: Difference of Squares
Count the number of terms. Is it a binomial?
Is the first term a perfect square?
Is the last term a perfect square?
Is it, or could it be, a subtraction of two perfect squares?
x2 – 9 = (x + 3)(x – 3)
The sum of squares will not factor a2+b2

4. Using FOIL we find the product of two binomials.

5. Rewrite the polynomial as the product of a sum and a difference.

6. Conditions for Difference of Squares
Must be a binomial with subtraction.
First term must be a perfect square.
(x)(x) = x2
Second term must be a perfect square (6)(6) = 36

7. Check for GCF.
Sometimes it is necessary to remove the GCF before it can be factored more completely.

8. Removing a GCF of -1.
In some cases removing a GCF of negative one will result in the difference of squares.

9. Difference of Squares
You Try

10. Factoring a perfect square trinomial in the form:

11. Perfect Square Trinomials can be factored just like other trinomials (guess and check), but if you recognize the perfect squares pattern, follow the formula!

12. a b
Does the middle term fit the pattern, 2ab?
Yes, the factors are (a + b)2 :

13. a b
Does the middle term fit the pattern, 2ab?
Yes, the factors are (a - b)2 :