7-6 Multiplying Polynomials Do you remember algebra tiles? Algebra 1 Glencoe McGraw-HillLinda Stamper

1 This piece is a 1 What is the total value of these pieces? 4 These pieces can be arranged differently. Changing the arrangement does not change the area!

This length is unknown. The width of this piece is 1. This piece is named by its area. This piece is an x. What is the total value of these pieces? 3x x

The length of this piece is x. The width of this piece is x. The area of this piece is x 2.

All of the yellow tiles we have used so far represent positive values. To represent negatives we will use the red side.

Write an expression for the following and solve. This is called the Zero Principle. Zero pairs cancel each other. Write an expression for the following and solve.

In previous lessons, you added polynomials Add the tiles.

x Algebra tiles can be used to model multiplying polynomials. The pieces of the rectangle inside the frame represent the product! Factors are represented on the outside of the factor frame!

x Negatives are represented by a red color.

(x+2) Today you will multiply a binomial by a binomial. The pieces of the rectangle inside the frame represent the product!

(x+2) When negatives are involved, beware of zero pairs! Remove zero pairs to find the product!

When not using algebra tiles, FOIL is a method used to multiply a binomial times a binomial. Plus multiply the Outer terms Using the distributive property Multiply the First terms Plus multiply the Inner terms Plus multiply the Last terms Combine like terms. F 0 I L

Find the product. Example 1 Example 2 Example 3 Example 4 Write an expression for the area of the designer rug.

Find the product. F 0 I L Example 1 Example 2 F 0 I L Change subtraction to addition to avoid sign errors.

Example 3 Find the product. F 0 I L Example 4 Write an expression for the area of the designer rug. Write formula for area of rectangle. F 0 I L Change subtraction to addition to avoid sign errors. The area of the rug is 6x 2 + x – 2 units 2.

The area of the trapezoid is units 2. The area A of a trapezoid is one half the height h times the sum of the bases, b 1 and b 2. Write an expression for the area of the trapezoid.

The area of a triangle is one half the base b times the height h. Write an expression for the area of the triangle. Example 5 Example 6

Example 5 The area of a triangle is one half the base b times the height h. Write an expression for the area of the triangle. The area of the triangle is 3x x – 14 units 2.

Example 6 The area of a triangle is one half the base b times the height h. Write an expression for the area of the triangle. The area of the triangle is 4x 2 - 2x – 2 units 2.

Find the product. Multiply a binomial with a trinomial. Change subtraction to addition. Distribute the 2x to the trinomial and then the -3.

Example 7 Find the product. Change subtraction to addition. Distribute the 6x to the trinomial and then the -5. Example 8 Find the product.

7-A7 Pages #18–31,34–39,68-73.

You can also multiply polynomials in a vertical format. Write in a vertical format – change subtraction to addition. Multiply –5 to the top polynomial Multiple 6x to the top polynomial Line up like terms vertically! Combine like terms.

Example 8 Use a vertical format to find the product. Line up like terms vertically!