Chapter 8.1, Problem 53PPS

a.

To determine

To state: What does the expression $\left(4x^2+2x-1\right)\left(2x^2-x+3\right)$ represent?

Answer to Problem 53PPS

The given expression represents the area of the rectangle.

Explanation of Solution

Given:

  

Calculation:

In the given rectangle, the length is given by the expression $\left(4x^2+2x-1\right)$ and the width is $\left(2x^2-x+3\right)$

Now, the area of the rectangle is given by

  $\text{Area = Length }\times \text{Width}$

Substituting values for length and width, the area of the rectangle is given by

  $\left(4x^2+2x-1\right)\left(2x^2-x+3\right)$

So, the given expression represents the area of the rectangle.

b.

To determine

To state: What does the expression $2\left(4x^2+2x-1\right)+2\left(2x^2-x+3\right)$ represent?

Answer to Problem 53PPS

The given expression represents the perimeter of the rectangle.

Explanation of Solution

Given:

  

Calculation:

In the given rectangle, the length is given by the expression $\left(4x^2+2x-1\right)$ and the width is $\left(2x^2-x+3\right)$

Now, the perimeter of the rectangle is given by

  $\text{Area = 2}\left(\text{Length}\right)\times 2\left(\text{Width}\right)$

Substituting values for length and width, the perimeter of the rectangle is given by

  $2\left(4x^2+2x-1\right)+2\left(2x^2-x+3\right)$

So, the given expression represents the perimeter of the rectangle.