Download presentation

1
**Multiplying Polynomials**

Distribute and FOIL

2
**Polynomials * Polynomials**

Multiplying a Polynomial by another Polynomial requires more than one distributing step. Multiply: (2a + 7b)(3a + 5b) Distribute 2a(3a + 5b) and distribute 7b(3a + 5b): 6a2 + 10ab 21ab + 35b2 Then add those products, adding like terms: 6a2 + 10ab + 21ab + 35b2 = 6a2 + 31ab + 35b2

3
**Polynomials * Polynomials**

An alternative is to stack the polynomials and do long multiplication. (2a + 7b) x (3a + 5b) (2a + 7b)(3a + 5b) (2a + 7b) x (3a + 5b) Multiply by 5b, then by 3a: When multiplying by 3a, line up the first term under 3a. 21ab + 35b2 + 6a2 + 10ab Add like terms: 6a2 + 31ab + 35b2

4
**Polynomials * Polynomials**

Multiply the following polynomials:

5
**Polynomials * Polynomials**

(x + 5) x (2x + -1) -x + -5 2x2 + 10x + 2x2 + 9x + -5 (3w + -2) x (2w + -5) -15w + 10 + 6w2 + -4w 6w w + 10

6
**Polynomials * Polynomials**

(2a2 + a + -1) x (2a2 + 1) 2a2 + a + -1 + 4a4 + 2a3 + -2a2 4a4 + 2a3 + a + -1

7
Types of Polynomials We have names to classify polynomials based on how many terms they have: Monomial: a polynomial with one term Binomial: a polynomial with two terms Trinomial: a polynomial with three terms

8
**(2x + -3)(4x + 5) = 8x2 + 10x + -12x + -15 = 8x2 + -2x + -15**

F.O.I.L. There is an acronym to help us remember how to multiply two binomials without stacking them. (2x + -3)(4x + 5) F : Multiply the First term in each binomial. 2x • 4x = 8x2 O : Multiply the Outer terms in the binomials. 2x • 5 = 10x I : Multiply the Inner terms in the binomials. -3 • 4x = -12x L : Multiply the Last term in each binomial. -3 • 5 = -15 (2x + -3)(4x + 5) = 8x2 + 10x + -12x = 8x2 + -2x + -15

9
**Use the FOIL method to multiply these binomials:**

1) (3a + 4)(2a + 1) 2) (x + 4)(x - 5) 3) (x + 5)(x - 5) 4) (c - 3)(2c - 5) 5) (2w + 3)(2w - 3)

10
**Use the FOIL method to multiply these binomials:**

1) (3a + 4)(2a + 1) = 6a2 + 3a + 8a + 4 = 6a2 + 11a + 4 2) (x + 4)(x - 5) = x2 + -5x + 4x = x2 + -1x + -20 3) (x + 5)(x - 5) = x2 + -5x + 5x = x 4) (c - 3)(2c - 5) = 2c2 + -5c + -6c + 15 = 2c c + 15 5) (2w + 3)(2w - 3) = 4w2 + -6w + 6w + -9 = 4w2 + -9

Similar presentations

© 2020 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google