Chapter 8, Problem 41CR

To determine

To find:An expression for the area of the rectangle as a product and as a polynomial in standard form.

Answer to Problem 41CR

  $(3x+5)(x+7)$

  $3x^2+26x+35$

Explanation of Solution

Given information:A rectangle has dimensions $3x+5\text{ and }x+7$ .

Calculation:The area of arectangle $=\text{length}\times \text{breadth}$

Then area of the rectangle with dimensions $3x+5\text{ and }x+7$ as a product,

  $(3x+5)(x+7)$

Then area of the rectangle with dimensions $3x+5\text{ and }x+7$ as a polynomial,

  $\begin{array}{l}(3x+5)(x+7)\\ =3x(x+7)+5(x+7)[\text{distributive property]}\\ \text{=}(3x)(x)+(3x)(7)+(5)(x)+(5)(7)[\text{distributive property]}\\ =3x^2+21x+5x+35\\ =3x^2+26x+35[\text{combining like terms]}\end{array}$