Section 3-2 Multiplying Polynomials

1. Section 3-2 Multiplying Polynomials Objectives Multiply Polynomials Use Binomial Expansion to expand binomial expressions that are raised to positive integer powers

2. Warm-Up ExamplesMultiply x(x3) 2(5x3) xy(7x2) 3x2(x5) x(6x2) 3y2(–3y)

3. How to Multiply a Polynomial and a Monomial To multiply a polynomial by a monomial, use the Distributive Property and the Properties of Exponents

4. Examples: Find the Product 4y2(y2+ 3) fg(f4 + 2f3g – 3f2g2 + fg3)

5. 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

6. Example: Multiply the Polynomials (a – 3)(2 – 5a + a2) (3b – 2c)(3b2 – bc – 2c2)

7. Example: Multiply the Polynomials (y2 – 7y + 5)(y2 – y – 3) (x2 – 4x + 1)(x2 + 5x – 2)

8. 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.

9. Expanding a Power of a Binomial (x + 4)4 (2x – 1)3

10. 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

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

12. Examples: Expand each expression (k – 5)3 (6m – 8)3 (x + 2)3 (3x + 1)4

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