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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 \begin{align*}W\end{align*}.

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

2. What is the area of the rectangle when \begin{align*}w = 6\end{align*}?

Now, change the width of the side by running the program again and enter a new value for \begin{align*}W\end{align*}.

3. What is the area of the rectangle when \begin{align*}w = 4\end{align*}? When \begin{align*}w = 9\end{align*}?

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

## Problem 2 - Areas of Small Rectangles

The rectangle at the right has dimensions \begin{align*}(x + 7)\end{align*} and rate of \begin{align*}(x + 2)\end{align*}. 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 \begin{align*}(x + 7)(x + 2)\end{align*} for \begin{align*}(AX+B)(CX+D)\end{align*}. \begin{align*}(A = 1, B = 7, C = 1, D = 2)\end{align*}

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 \begin{align*}(3x + 5)\end{align*} and \begin{align*}(6x + 2)\end{align*}?

9. a. \begin{align*}(4x + 1)(3x + 9)\end{align*}

b. \begin{align*}(x + 8)(7x + 3)\end{align*}

c. \begin{align*}(2x + (-3))(5x + 8)\end{align*}

## Homework/Extensions

1. a. \begin{align*}(4x + 2)(x + 7) =\end{align*}

b. \begin{align*}(3x - 7)(2x + 4) =\end{align*}

c. \begin{align*}(2x + 5)(6x + 1) =\end{align*}

d. \begin{align*}(5x + 3)(9x - 2) =\end{align*}

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 \begin{align*}a, b, c, d,\end{align*} and \begin{align*}e\end{align*} 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 \begin{align*}(1x^2 + 3x + 4)\end{align*} and \begin{align*}(5x + 6)\end{align*}?

5. a. \begin{align*}(2x^2 + 1x + 7)(3x + (-6)) = \end{align*}

b. \begin{align*}(4x^2 + 3x + 8)(x + 3) = \end{align*}

c. \begin{align*}(2x^2 + 6x + 4)(-3x + 9) =\end{align*}

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