1. Factoring Sums and Differences
Section 9.8

2. Sums and Differences of Cubes
x3 + y3 = (x + y) (x2 – xy + y2)
x3 - y3 = (x - y) (x2 + xy + y2)

3. For general odd powers…
xn + yn = (x + y) (xn-1 – xn-2 y + xn-3y2 - … - xyn-2 + yn-1)
xn - yn = (x - y) (xn-1 + xn-2 y + xn-3y2 + … + xyn-2 + yn-1)

4. Find the fourth roots of 16.
Example 1
Find the fourth roots of 16.
x = 0
(x2 + 4)(x2 – 4)
x = 2i , x = -2i
x = 2 , x = -2

5. Example 2
Factor x3 – 64y12 over the set of polynomial with rational coefficients
(x – 4y4)(x2 + 4xy4 + 16y8)

6. Factor m6 + n6 over the set of polynomial with rational coefficients.
Example 3
Factor m6 + n6 over the set of polynomial with rational coefficients.
Same as (m2 + n2)3
(m2 + n2)(m4 – m2n2 + n4)

7. Example 4
Factor x10 – y10 completely over the set of polynomials with rational coefficients.
Same as (x5 – y5)2
(x5 – y5)(x5 + y5)
(x – y)(x4 +x3y + x2y2 + xy3 + y4)
(x + y )(x4 - x3y + x2y2 - xy3 + y4)

8. Homework
Pages 605 – 606
4 - 7,