Chapter 8.2, Problem 52PFA

To determine

Towrite: The equivalent expression for the next step.

Answer to Problem 52PFA

D. $3x^2+15x+36x-8x+4x^2$

Explanation of Solution

Given:

The expression $3x\left(x^2+5x+12\right)-4x\left(2-x\right)$ .

Calculation:

The next step of the simplification would be to distribute the expressions over parentheses. So, the equivalent form of the next step will be as follows:

  $\begin{array}{c}\left(x^2+5x+12\right)-4x\left(2-x\right)=3x\cdot x^2+3x\cdot 5x+3x\cdot 12-4x\cdot 2-4x\left(-x\right)\\ =3x^2+15x+36x-8x+4x^2\end{array}$

Therefore, the correct option for the equivalent expression is D. $3x^2+15x+36x-8x+4x^2$ .