Title: Finding the Area of a StampDescription: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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Answered: Find the area of the stamp when / = 4x…

Math

Algebra

Find the area of the stamp when / = 4x – 1 and w = 2x + 1. (Simplify your answer completely.) cm2 I cm w cm USA

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

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