1. ALGEBRA 1 Lesson 8-2 Warm-Up

2. ALGEBRA 1 This is an area model using Algebra Tiles. Simply model 3x + 1 on the top (length of rectangle) and 2x on the side (width of rectangle). Then, fill in the rectangular area made by this product with x 2, x, and 1 tiles. “Multiplying and Factoring” (8-2) How do you multiply a monomial and a binomial or trinomial? To multiply a monomial and a binomial or trinomial, use the distributive property or an area model Examples: Simplify 2x (3x + 1). Method 1: Use the Distributive Property 2x(3x + 1) = 2x(3x) + 2x (1) = 6x 2 + 2x Method 2: Use an Area Model (write the product of each row and column in the box where they intersect, or cross) 3x + 1 2x = 6x 2 + 2x 2x 3x = 6x 2 2x 1 = 2x x x x x x 1 x x x2x2 x2x2 x2x2 x2x2 x2x2 x2x2 x2x2 x x1 x x 1 11

3. ALGEBRA 1 Simplify –2g 2 (3g 3 + 6g – 5). –2g 2 (3g 3 + 6g – 5) = –2g 2 (3g 3 ) + –2g 2 (6g) – (–2g 2 )(5) Use the Distributive Property. = –6g 2 + 3 – 12g 2 + 1 + 10g 2 Multiply the coefficients and add the exponents of powers with the same base. = –6g 5 – 12g 3 + 10g 2 Simplify. Multiplying and Factoring LESSON 8-2 Additional Examples

4. ALGEBRA 1 “Multiplying and Factoring” (8-2) How do you find a common factor of a polynomial? To find a common multiple of a polynomial, multiply the common factors (factors all terms have in them) together. Example: Find the common factor of the terms 4x 3 + 12x 2 – 8x. The common factor is 2 2 x or 4x.

5. ALGEBRA 1 Find the common factor of 2x 4 + 10x 2 – 6x. List the prime factors of each term. Identify the factors common to all terms. 2x 4 = 2 x x x x 10x 2 = 2 5 x x 6x = 2 3 x The common factor is 2 x, or 2x. Multiplying and Factoring LESSON 8-2 Additional Examples

6. ALGEBRA 1 Factor 4x 3 – 8x 2 + 12x. Step 1: Find the common factor. 4x 3 = 2 2 x x x 8x 2 = 2 2 2 x x 12x = 2 2 3 x Step 2: Factor out the common factor. 4x 3 – 8x 2 + 12x = 4x(x 2 ) + 4x(–2x) + 4x(3) = 4x(x 2 – 2x + 3) The common factor is 2 2 x or 4x. Multiplying and Factoring LESSON 8-2 Additional Examples

7. ALGEBRA 1 1.Simplify –2x 2 (–3x 2 + 2x + 8). 2. Find the common factor of 16b 4 – 4b 3 + 8b 2. 3.Factor 3x 3 + 9x 2. 4.Factor 10y 3 + 5y 2 – 15y. 6x 4 – 4x 3 – 16x 2 4b24b2 3x 2 (x + 3) 5y(2y 2 + y – 3) Multiplying and Factoring LESSON 8-2 Lesson Quiz