Chapter 8.3, Problem 48PPE

To determine

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

Answer to Problem 48PPE

  $54a^2+36a+6$

Explanation of Solution

Given information:The side length of the cube is $3a+1$ .

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

Then, surface area of the cube with side length $3a+1$ is,

  $\begin{array}{l}$ 6{(3a+1)}^2$$ =6(9a^2+6a+1)[\because {(a+b)}^2=a^2+2ab+b^2]$=6(9a^2)+6(6a)+6(1)[\text{distributive law]}\\ =54a^2+36a+6\end{array}$

Thus, the surface area is $54a^2+36a+6$ .