1. Factoring Special Forms
Chapter 5 Section 5
Factoring Special Forms

2. Factoring Difference of Two Squares
Two ways
Area model
Rule

3. Factor 9x
Area model: set up 9x2 – 100 9x2 + 0x – 100 Sum is 0, product is Two numbers are 30 and - 30

4. Factor 9x
Rewrite as the difference of two squares 9x2 is (3x)2 100 is 102 So (3x) Rule: Factor the difference of two square as the product of the sum and difference of the those terms. Thus: (3x – 10)(3x+ 10)

5. Caution
Be sure that you factor the common factor before factoring

6. Try
4x2 – 9
2x3 – 8x

7. Repeated Factorization
Try: 81x4 – 16
Note: After you factor, look at the factors.

8. Factoring Perfect Square Trinomials
Two ways
Area Model
Rule

9. Check for a Perfect Square Trinomial
Middle (linear) term is twice the product of the outside terms that are being squared.
Example: 4x2 + 12xy + 9y2
leading term: (2x)2
Last term: (3y)2
Multiply the expression being square and multiply by 2
2(2x)(3y) which is the middle term.

10. Factor: 4x2 + 12xy + 9y2 Since it is a perfect square trinomial
Factor: Take the terms being squared in order and write as a binomial with the first sign and square the binomial.
(2x + 3y)2

11. Factor: 4x2 + 12xy + 9y2 Set up for the area model
Sum is 12, product is (4)(9)
Numbers are 6xy and 6xy

12. Sum or Difference of Two Cube
Observe:
(A + B)3 = (A + B)(A2 - AB + B2)
(A - B)3 = (A - B)(A2 + AB + B2)
Words: Write the binomial, then square the first, change the signs, multiply together and square the second.

13. Factor: x
Rewrite as the sum of cubes
(x)3 + (5)3

14. Try
25x4 – 25y6
2x3y – 18xy
25y2 – 10y + 1
27x3 - 8

15. Summary Binomial Trinomial Difference of two squares
Sum or Difference of two cubes
Trinomial
Area model
Grouping
Perfect square trinomial