Lesson 3: 8-3 Multiplying Polynomials

How do you determine the new term after multiplying two terms of polynomial?
How do you know you have finished the multiplication?
What are like terms?
How do you combine like terms?

FOIL method
quadratic expression

A.APR.1 Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtarction, and multiplication; add, subtract, and multiply polynomials.

SAT questions related to multiplying binomials: 4-3-5, 6-3-15, 4-4-28, 5-4-35, 8-3-5, 1-3-15;

The FOIL method only works for multiplying two binomials. Use the Distributive Property to multiply other polynomials. To use the FOIL method, find the sum of the products of the first terms (F), the outer terms (O), the inner terms (I), and the last terms (L).

Bodyboards, which are used to ride waves, are made of foam and are more rectangular than surfboards. A bodyboard's dimensions are determined by the height and skill level of the user.
The length of Ann's bodyboard should be Ann's height h minus 32 inches or h-32. The board's width should be half of Ann's height plus 11 inches or 1/2h+11. To approximate the area of the bodyboard, you need to find (h-32)(1/2h+11).

When students multiply polynomials horizontally, they often try to combine terms that are not like terms. For students who are having difficulty suggest that they try multiplying the polynomials in vertical form, aligning like terms.

If students are less familiar with the Distributive Property, then they may wish to use the vertical method of multiplying two-digit numbers. Suggest that students use the method with which they are most comfortable.

Practice: Exercises 1 -11

Exercises 50-59

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