Chapter 8.3, Problem 47PPE

To determine

To find:A polynomial in standard form for the surface area of each cube.

Answer to Problem 47PPE

  $6x^2+24x+24$

Explanation of Solution

Given information:The side length of the cube is $x+2$ .

Calculation:The surface area of a cube with side a is $6a^2$ .

Then, surface area of the cube with side length $x+2$ is,

  $\begin{array}{l}$ 6{(x+2)}^2$$ =6(x^2+4x+4)[\because {(a+b)}^2=a^2+2ab+b^2]$=6(x^2)+6(4x)+6(4)[\text{distributive law]}\\ =6x^2+24x+24\end{array}$

Thus, the surface area is $6x^2+24x+24$ .