OBJECTIVESMULTIPLY POLYNOMIALS

USE BINOMIAL EXPANSION TO EXPAND BINOMIAL EXPRESSIONS THAT ARE

RAISED TO POSITIVE INTEGER POWERS

Section 3-2 Multiplying Polynomials

Warm-Up ExamplesMultiply

x(x3)

2(5x3)

xy(7x2)

3x2(x5)

x(6x2)

3y2(–3y)

How to Multiply a Polynomial and a Monomial

To multiply a polynomial by a monomial, use the Distributive Property and the Properties of Exponents

Examples: Find the Product

4y2(y2 + 3)

fg(f4 + 2f3g – 3f2g2 + fg3)

Multiplying Polynomials

To multiply any two polynomials, use the Distributive Property and multiply each term in the second polynomial by each term in the first polynomial

Keep in mind that if one polynomial has m terms and the other has n terms, then the product has mn terms before it is simplified

Example: Multiply the Polynomials

(a – 3)(2 – 5a + a2)

(3b – 2c)(3b2 – bc – 2c2)

Example: Multiply the Polynomials

(y2 – 7y + 5)(y2 – y – 3)

(x2 – 4x + 1)(x2 + 5x – 2)

Business Application

A standard Burly Box is p feet by 3p feet by 4p feet. A large Burly Box has 1.5 foot added to each dimension. Write a polynomial V(p) in standard form that can be used to find the volume of a large Burly Box.

Expanding a Power of a Binomial

(x + 4)4

(2x – 1)3

Pascal’s Triangle

Notice the coefficients of the variables in the final product of (a + b)3. These coefficients are the numbers from the third row of Pascal’s Triangle.

Each row of Pascal’s Triangle gives the coefficients of the corresponding binomial expansion. The pattern in the table can be extended to apply to the expansion of any binomial of the form (a + b)n, where n is a whole number

Binomial Expansion

This information is formalized by the Binomial Theorem, which will be studied further in Chapter 11

Examples: Expand each expression

(k – 5)3

(6m – 8)3

(x + 2)3

(3x + 1)4

Homework

Pages 162-164 #18-34, #39-56, and #58-66