Unit 1 Algebra Skills Review Lesson 1 Polynomials

Unit 1: Algebra Skills Review

Lesson 1: Polynomials & Special Products

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?

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.

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

• 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?

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

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

Special Product Patterns u and v are variables that represent a monomial (or even another polynomial). 1. (u + v)(x – v) = u 2 – v 2 2. (u + v)2 = u 2 + 2 uv + v 2 3. (u – v)2 = u 2 – 2 uv + v 2 4. (u + v)3 = u 3 + 3 u 2 v + 3 uv 2 + v 3 5. (u – v)3 = u 3 – 3 u 2 v + 3 uv 2 – v 3

11. (x + 2)3 12. (2 x – 3)3

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

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

Homework • Complete Unit 1, Lesson 1 Exercises

Homework: Unit 1 – Lesson 1 Exercises Visit: www. vrwilkeskhs. pbworks. com