Warm – up Add or subtract the following polynomials 1.(x 3 + 3x – 4) + (5x 3 – 2x 2 - 8x) 2.(6x 3 -6x ) - (11x 3 – 9x 2 - x)

Multiplying Polynomials and Special Products

Standards MM1A2. Students will simplify and operate with radical expressions, polynomials, and rational expressions. –Add, subtract, multiply, and divide polynomials. –Use the binomial theorem to expand polynomials. –g. Use area and volume models for polynomial arithmetic. MM1G2. Students will understand and use the language of mathematical argument and justification. –Use conjecture, inductive reasoning, deductive reasoning, counterexamples, and indirect proof as appropriate.

Essential Question Unit: In what ways can algebraic methods be used in problem solving? Lesson: What are the ways we can expand/multiply polynomials?

Example 1 Find the product 6(4a + 7) = 24a + 42

Example 2 Find the product 5mn 2 (3m – 4n) = 15m 2 n 2 – 20mn 3

Example 3 -10pq(4pq + 4p – 3q 2 ) = -40p 2 q 2 – 40p 2 q + 30pq 3

Multiplying 2 Binomials To multiply two binomials, we can use the FOIL method. F – First O – Outer I – Inner L - Last

Example 1 Find the product (a + 3)(a + 5) = a 2 + 5a + 3a + 15 = a 2 + 8a + 15

Example 2 Find the product (2x 2 + 4)(3x + 1) = 6x 3 + 2x x + 4

Multiplying with an area model (x + 6)(x – 3) (2x – 1)( 5x 2 + 2x)

You Try! a.(5x – 2)(x – 6) b.(x + 5)(x 2 + 4x) Solutions: a.5x 2 – 32x + 12 b.x 3 + 9x x

Example 3 Find the product (x – 3)(x 2 + 7x + 5) = x 3 + 7x 2 + 5x – 3x 2 – 21x – 15 = x 3 + 4x 2 – 16x – 15 We technically can’t use the FOIL method, but we follow a similar process!

Example 4 Find the product. (7x + y) 2 = (7x + y)(7x + y) = 49x 2 + 7xy + 7xy + y 2 = 49x xy + y 2

You Try! a.(x – 6)(x 2 + 6x + 8) b.(5b – 7c) 2 Solutions: a.x 3 – 28x – 48 b.25b 2 – 70bc + 49c 2

Example 5 (x – 2 ) (x + 2) x 2 – 2x + 2x - 4 X 2 - 4

DivisionDivision

Classwork Worksheet

Homework Page 67 –Numbers 2 – 20 evens Page 157 Practice Guide –Numbers 1-4