1. 2.2 Warm Up Find the sum or difference. 1. (2x – 3 + 8x²) + (5x + 3 – 8x²) 2. (x³ - 5x² - 4x) – (4x³ - 3x² + 2x – 8) 3. (x – 4) – (5x³ - 2x² + 3x – 11)

2. 2.2 Multiplying Polynomials

3. Multiplying a monomial & a polynomial Distribute the monomial to each term in the polynomial Distribute the monomial to each term in the polynomial 3x 2 (7x 2 -2x+3) 3x 2 (7x 2 ) + 3x 2 (-2x) + 3x 2 (3) Multiply the coefficients and add exponents when multiplying like bases. 21x 4 – 6x 3 + 9x 2

4. Examples: 1. x²(6x² - 3x – 1) 2. -5x³(4x 4 – 3x + 1) 3. 4x²(-2x³ + 5x² - 6x + 2)

5. Multiplying polynomials Distribute each term in the 1 st polynomial to each term in the 2 nd polynomial Distribute each term in the 1 st polynomial to each term in the 2 nd polynomial 1. (x 2 + 6x +4)(3x - 1) x²(3x) + 6x(3x) + 4(3x) + x²(-1) + 6x(-1) + 4(-1) 3x³ + 18x² + 12x + -x² + -6x + -4 3x³ + 18x² + 12x + -x² + -6x + -4 3x³ + 17x² + 6x - 4 2. (2x² - x + 6)(x + 7) 3. (2x + 5)(x² + 3x – 1)

6. FOIL Method (used for 2 binomials) FOIL method with Binomials is still distributing each term!!! F (first terms) O (outside terms) I (inside terms) L (last terms in each binomial) 1. (2n + 7)(2n + 4) O L F I 2n(2n) + 2n(4) + 7(2n) + 7(4) 4n² + 8n + 14n + 28 4n² + 22n + 28

7. FOIL Examples 1. (6x – 3)(4x – 1) 2. (8x – 3)(2x + 2) 3. (4x² + 4)(-2x² - 8) 4. (x – 3)(4x + 5)