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# 10.1: FOILed Again

Difficulty Level: At Grade Created by: CK-12

This activity is intended to supplement Algebra I, Chapter 9, Lesson 2.

## Problem 1 - Introduction to Area of a Rectangle

Run the AREA program (in PRGM) and select the option for Problem 1 (#1).

Enter 6 for $W$.

1. What are the lengths of the sides of the rectangle?

2. What is the area of the rectangle when $w = 6$?

Now, change the width of the side by running the program again and enter a new value for $W$.

3. What is the area of the rectangle when $w = 4$? When $w = 9$?

4. Explain how the expression for the area is simplified.

## Problem 2 - Areas of Small Rectangles

The rectangle at the right has dimensions $(x + 7)$ and rate of $(x + 2)$. Each piece of the rectangle is a different color so that you can focus on its area.

5. What is the area of each small rectangle?

6. What is the total area of the rectangle?

## Problem 3 - FOIL Method

Run the AREA program and select the option for Problem 3.

Enter $(x + 7)(x + 2)$ for $(AX+B)(CX+D)$. $(A = 1, B = 7, C = 1, D = 2)$

7. How do the areas of the small rectangles in Problem 2 relate to the expression shown on the bottom of the screen?

Practice finding the area of a rectangle and then check your answers with the program.

8. What is the expression of the area of a rectangle with dimensions $(3x + 5)$ and $(6x + 2)$?

9. a. $(4x + 1)(3x + 9)$

b. $(x + 8)(7x + 3)$

c. $(2x + (-3))(5x + 8)$

## Homework/Extensions

1. a. $(4x + 2)(x + 7) =$

b. $(3x - 7)(2x + 4) =$

c. $(2x + 5)(6x + 1) =$

d. $(5x + 3)(9x - 2) =$

Next, you will be multiplying a trinomial (3 terms) times a binomial (2 terms) to find the area of a rectangle.

2. What method can you use to find the simplified expression for the area?

3. Use the letters $a, b, c, d,$ and $e$ to determine the formula used to find the 6 terms of area shown at the right.

4. What is the area of the rectangle with dimensions $(1x^2 + 3x + 4)$ and $(5x + 6)$?

5. a. $(2x^2 + 1x + 7)(3x + (-6)) =$

b. $(4x^2 + 3x + 8)(x + 3) =$

c. $(2x^2 + 6x + 4)(-3x + 9) =$

Feb 22, 2012

Oct 31, 2014