Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
![Title: Finding the Area of a Stamp
Description:
This tutorial will guide you through the process of finding the area of a rectangular stamp using given expressions for its length and width, and then simplifying the expression.
Problem Statement:
Find the area of the stamp when \( l = 4x - 1 \) and \( w = 2x + 1 \). (Simplify your answer completely.)
Steps to Solve:
1. Formula for Area:
The area \( A \) of a rectangle is determined by the formula:
\[
A = l \times w
\]
where \( l \) represents the length and \( w \) represents the width.
2. Substitute the Given Expressions:
Substitute the given expressions for \( l \) and \( w \) into the area formula:
\[
A = (4x - 1)(2x + 1)
\]
3. Distribute to Simplify:
Use the distributive property (also known as FOIL for binomials) to multiply the expressions:
\[
A = (4x - 1)(2x + 1)
\]
\[
A = 4x \cdot 2x + 4x \cdot 1 - 1 \cdot 2x - 1 \cdot 1
\]
4. Combine Like Terms:
Simplify the resulting expression by combining like terms:
\[
A = 8x^2 + 4x - 2x - 1
\]
\[
A = 8x^2 + 2x - 1
\]
5. Final Area Expression:
The simplified expression for the area of the stamp is:
\[
A = 8x^2 + 2x - 1 \quad \text{cm}^2
\]
Diagram Description:
The diagram included provides a visual representation of a postage stamp. It shows the length (\( l \)) and width (\( w \)) of the stamp in centimeters.
- The length is depicted vertically and labeled as \( l \) cm.
- The width is depicted horizontally and labeled as \( w \) cm.
- The diagram includes the expressions \( l = 4x - 1 \) and \( w = 2x + 1 \) to be used in](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4c02ecae-9f3c-4011-90ce-878cb1c02c8e%2F66405eca-9a1d-4494-94a1-2745c4fb775f%2F9wleaf_processed.png&w=3840&q=75)
Transcribed Image Text:Title: Finding the Area of a Stamp
Description:
This tutorial will guide you through the process of finding the area of a rectangular stamp using given expressions for its length and width, and then simplifying the expression.
Problem Statement:
Find the area of the stamp when \( l = 4x - 1 \) and \( w = 2x + 1 \). (Simplify your answer completely.)
Steps to Solve:
1. Formula for Area:
The area \( A \) of a rectangle is determined by the formula:
\[
A = l \times w
\]
where \( l \) represents the length and \( w \) represents the width.
2. Substitute the Given Expressions:
Substitute the given expressions for \( l \) and \( w \) into the area formula:
\[
A = (4x - 1)(2x + 1)
\]
3. Distribute to Simplify:
Use the distributive property (also known as FOIL for binomials) to multiply the expressions:
\[
A = (4x - 1)(2x + 1)
\]
\[
A = 4x \cdot 2x + 4x \cdot 1 - 1 \cdot 2x - 1 \cdot 1
\]
4. Combine Like Terms:
Simplify the resulting expression by combining like terms:
\[
A = 8x^2 + 4x - 2x - 1
\]
\[
A = 8x^2 + 2x - 1
\]
5. Final Area Expression:
The simplified expression for the area of the stamp is:
\[
A = 8x^2 + 2x - 1 \quad \text{cm}^2
\]
Diagram Description:
The diagram included provides a visual representation of a postage stamp. It shows the length (\( l \)) and width (\( w \)) of the stamp in centimeters.
- The length is depicted vertically and labeled as \( l \) cm.
- The width is depicted horizontally and labeled as \( w \) cm.
- The diagram includes the expressions \( l = 4x - 1 \) and \( w = 2x + 1 \) to be used in
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