2.2 Warm Up2.2 Warm UpFind the sum or difference.Find the sum or difference.

1. (2x – 3 + 8x1. (2x – 3 + 8x²) + (5x + 3 – 8x²)²) + (5x + 3 – 8x²)

2. (x³ - 5x² - 4x) – (4x³ - 3x² + 2x – 8)2. (x³ - 5x² - 4x) – (4x³ - 3x² + 2x – 8)

3. (x – 4) – (5x³ - 2x² + 3x – 11)3. (x – 4) – (5x³ - 2x² + 3x – 11)

2.2 Multiplying Polynomials2.2 Multiplying Polynomials

Multiplying a monomial & a Multiplying a monomial & a polynomialpolynomial

Distribute the monomial to each Distribute the monomial to each term in the polynomialterm in the polynomial3x3x22(7x(7x22-2x+3)-2x+3)3x3x22 (7x (7x22) + 3x) + 3x2 2 (-2x)(-2x) + + 3x3x2 2 (3)(3)

Multiply the coefficients andMultiply the coefficients andadd exponents when multiplying like add exponents when multiplying like

bases.bases.21x21x44 – 6x – 6x33 + 9x + 9x2 2

Examples:Examples:1. x1. x²(6x² - 3x – 1)²(6x² - 3x – 1)

2. -5x³(4x2. -5x³(4x44 – 3x + 1) – 3x + 1)

3. 4x²(-2x³ + 5x² - 6x + 2)3. 4x²(-2x³ + 5x² - 6x + 2)

Multiplying polynomialsMultiplying polynomials Distribute each term in the 1Distribute each term in the 1stst polynomial polynomial

to each term in the 2to each term in the 2ndnd polynomial polynomial

1.1. (x(x2 2 + 6x +4)(3x - 1)+ 6x +4)(3x - 1)

xx²(3x) + 6x(3x) + 4(3x) + x²(-1) + 6x(-1) + 4(-1)²(3x) + 6x(3x) + 4(3x) + x²(-1) + 6x(-1) + 4(-1)

3x³ + 18x² + 12x + -x² + -6x + -43x³ + 18x² + 12x + -x² + -6x + -4

3x³ + 17x² + 6x - 43x³ + 17x² + 6x - 4

2.2. (2x(2x² - x + 6)(x + 7)² - x + 6)(x + 7)

3.3. (2x + 5)(x² + 3x – 1)(2x + 5)(x² + 3x – 1)

FOIL Method (used for 2 binomials)FOIL Method (used for 2 binomials)FOIL method with Binomials is still FOIL method with Binomials is still

distributing each term!!!distributing each term!!!

F (first terms) O (outside terms) I (inside F (first terms) O (outside terms) I (inside terms) L (last terms in each binomial)terms) L (last terms in each binomial)

1.1. (2n + 7)(2n + 4)(2n + 7)(2n + 4)

OL

F I

2n(2n) + 2n(4) + 7(2n) + 7(4)

4n² + 8n + 14n + 28

4n² + 22n + 28

FOIL ExamplesFOIL Examples1.1. (6x – 3)(4x – 1)(6x – 3)(4x – 1)

2.2. (8x – 3)(2x + 2)(8x – 3)(2x + 2)

3.3. (4x(4x² + 4)(-2x² - 8)² + 4)(-2x² - 8)

4.4. (x – 3)(4x + 5)(x – 3)(4x + 5)