<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />

# 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\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 w=6\begin{align*}w = 6\end{align*}?

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

3. What is the area of the rectangle when w=4\begin{align*}w = 4\end{align*}? When w=9\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 (x+7)\begin{align*}(x + 7)\end{align*} and rate of (x+2)\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 (x+7)(x+2)\begin{align*}(x + 7)(x + 2)\end{align*} for (AX+B)(CX+D)\begin{align*}(AX+B)(CX+D)\end{align*}. (A=1,B=7,C=1,D=2)\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 (3x+5)\begin{align*}(3x + 5)\end{align*} and (6x+2)\begin{align*}(6x + 2)\end{align*}?

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

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

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

## Homework/Extensions

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

b. (3x7)(2x+4)=\begin{align*}(3x - 7)(2x + 4) =\end{align*}

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

d. (5x+3)(9x2)=\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 a,b,c,d,\begin{align*}a, b, c, d,\end{align*} and e\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 (1x2+3x+4)\begin{align*}(1x^2 + 3x + 4)\end{align*} and (5x+6)\begin{align*}(5x + 6)\end{align*}?

5. a. (2x2+1x+7)(3x+(6))=\begin{align*}(2x^2 + 1x + 7)(3x + (-6)) = \end{align*}

b. (4x2+3x+8)(x+3)=\begin{align*}(4x^2 + 3x + 8)(x + 3) = \end{align*}

c. (2x2+6x+4)(3x+9)=\begin{align*}(2x^2 + 6x + 4)(-3x + 9) =\end{align*}

### Notes/Highlights Having trouble? Report an issue.

Color Highlighted Text Notes

Show Hide Details
Description
Tags:
Subjects: