Chapter 8.3, Problem 53PFA

To determine

To find: The expression which is equivalent to square of $4x+8$

Answer to Problem 53PFA

The square of the given expression is $16x^2+64x+64$

D is the correct option.

Explanation of Solution

Given:

The expression is $4x+8$

Options are

  $\begin{array}{l}\mathrm{A }8x+16\\ \mathrm{B }16x^2+64\\ \mathrm{C }16x^2+24x+64\\ \mathrm{D }16x^2+64x+64\end{array}$

Calculation:

The expression is $4x+8$

Find the square of this expression ${\left(4x+8\right)}^2$

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

  $\begin{array}{l}{\left(4x+8\right)}^2\\ ={\left(4x\right)}^2+2\cdot 4x\cdot 8+8^2\\ =16x^2+64x+64\end{array}$

So, the square of the given expression is $16x^2+64x+64$

D is the correct option.