Chapter 8.4, Problem 40PPS

To determine

To find: The product ${\left(\frac{3}{4}k+8\right)}^2$

Answer to Problem 40PPS

  $\frac{9}{16}{k}^2+12k+64$

Explanation of Solution

Given:

  ${\left(\frac{3}{4}k+8\right)}^2$

Calculation:

The given expression is ${\left(\frac{3}{4}k+8\right)}^2$

Apply the formula ${\left(a+b\right)}^2=a^2+2ab+b^2$ and then simplify

  $\begin{array}{l}{\left(\frac{3}{4}k+8\right)}^2\\ ={\left(\frac{3}{4}k\right)}^2+2\cdot \frac{3}{4}k\cdot 8+{\left(8\right)}^2\\ =\frac{9}{16}{k}^2+12k+64\end{array}$