1. Unit 1: Algebra Skills Review

2. Lesson 1: Polynomials & Special Products

3. Lesson 1: Polynomials and Special Products
Today’s Essential Questions:
What does it mean to simplify an expression?
How can you tell when to combine like terms vs. when to use the distribute property?
Can you use patterns to help you simplify certain special products more efficiently?

4. K-W-L
As a team, discuss and write what already know about this topic in column 1 and what you want to learn in column 2.

5. Examples: Simplify each expression. 1
Examples: Simplify each expression (4x3 – x2 + 3x) – (x3 + 12x – 3) 2. (x4 + x2 – 3x + 7) + (2x2 – 5x – 12) 3. (3x + 2)(4x – 5) 4. (x2 – 4x + 3)(x2 + 4x + 5)

6. So what does it mean to simplify an expression?
How do you know when to combine like terms and when to use the distributive property?

7. Examples: Simplify
5. (x + 8)(x – 8)
6. (x – 3)(x + 3)
7. (2x + 5)(2x – 5)
Do you notice a pattern? Explain.

8. Examples: Simplify
8. (x + 8)2
9. (x – 3)2
10. (2x + 5)2
Do you notice a pattern? Explain.

9. Special Product Patterns
u and v are variables that represent a monomial (or even another polynomial).
(u + v)(x – v) = u2 – v2
(u + v)2 = u2 + 2uv + v2
(u – v)2 = u2 – 2uv + v2
(u + v)3 = u3 + 3u2v + 3uv2 + v3
(u – v)3 = u3 – 3u2v + 3uv2 – v3

10. 11. (x + 2)3
12. (2x – 3)3

11. You try:
13. (3x + 2)3
14. (2x – 1)3

12. K-W-L
As a team, discuss and write what you learned today in the third column.

13. Homework
Complete Unit 1, Lesson 1 Exercises

14. Unit 1 – Lesson 1 Exercises
Homework:
Unit 1 – Lesson 1 Exercises
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