Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.
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### Problem Statement: Find a polynomial that represents the area of the square when \( a = 2 \) and \( b = 3 \). (Simplify your answer completely.) ### Visual Description: - The image shows a square with side lengths labeled as \( (ax + b) \) feet. - There is an empty bracket where the side length of the square can be filled in. This is followed by \( \text{ft}^2 \) indicating the units of area. ### Diagram Explanation: - **Square Diagram:** - **Side Lengths:** Each side of the square is denoted as \( (ax + b) \) feet. - **Notation:** \( a \) and \( b \) are variables, which are provided values in the problem statement. Here, \( a = 2 \) and \( b = 3 \). ### Steps to Solve the Problem: 1. **Determine the Side Length of the Square:** - Given \( a = 2 \) and \( b = 3 \), substitute these values into \( (ax + b) \): \[ \text{Side Length} = 2x + 3 \text{ ft} \] 2. **Calculate the Area of the Square:** - The area \( A \) of a square is given by squaring the side length: \[ A = (2x + 3)^2 \] 3. **Expand the Polynomial:** - Apply the binomial expansion formula to \( (2x + 3)^2 \): \[ (2x + 3)^2 = (2x + 3)(2x + 3) \] \[ = 4x^2 + 6x + 6x + 9 \] \[ = 4x^2 + 12x + 9 \] 4. **Conclusion:** - The polynomial that represents the area of the square is: \[ 4x^2 + 12x + 9 \text{ ft}^2 \] ### Final Answer: \[ 4x^2 + 12x + 9 \text{ ft}^2 \]
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Transcribed Image Text:### Problem Statement: Find a polynomial that represents the area of the square when \( a = 2 \) and \( b = 3 \). (Simplify your answer completely.) ### Visual Description: - The image shows a square with side lengths labeled as \( (ax + b) \) feet. - There is an empty bracket where the side length of the square can be filled in. This is followed by \( \text{ft}^2 \) indicating the units of area. ### Diagram Explanation: - **Square Diagram:** - **Side Lengths:** Each side of the square is denoted as \( (ax + b) \) feet. - **Notation:** \( a \) and \( b \) are variables, which are provided values in the problem statement. Here, \( a = 2 \) and \( b = 3 \). ### Steps to Solve the Problem: 1. **Determine the Side Length of the Square:** - Given \( a = 2 \) and \( b = 3 \), substitute these values into \( (ax + b) \): \[ \text{Side Length} = 2x + 3 \text{ ft} \] 2. **Calculate the Area of the Square:** - The area \( A \) of a square is given by squaring the side length: \[ A = (2x + 3)^2 \] 3. **Expand the Polynomial:** - Apply the binomial expansion formula to \( (2x + 3)^2 \): \[ (2x + 3)^2 = (2x + 3)(2x + 3) \] \[ = 4x^2 + 6x + 6x + 9 \] \[ = 4x^2 + 12x + 9 \] 4. **Conclusion:** - The polynomial that represents the area of the square is: \[ 4x^2 + 12x + 9 \text{ ft}^2 \] ### Final Answer: \[ 4x^2 + 12x + 9 \text{ ft}^2 \]
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