Chapter 8.2, Problem 52PFA

To determine

To choose: The equivalent form for written for student.

Answer to Problem 52PFA

The equivalent expression is $3x^3+15x^2+36x-8x+4x^2$

D is the correct option.

Explanation of Solution

Given:

The first step is $3x\left(x^2+5x+12\right)-4x\left(2-x\right)$

Options are

  $\begin{array}{l}\mathrm{A }.3x\left(18x^3\right)+4x\left(x\right)\\ \mathrm{B }.3x\left(60x^3\right)+4x\left(-2x\right)\\ \mathrm{C }.3x^3+15x^2+36-8x-4x^2\\ \mathrm{D }.3x^3+15x^2+36x-8x+4x^2\end{array}$

Calculation:

The first step is given by the expression $3x\left(x^2+5x+12\right)-4x\left(2-x\right)$

Use distributive property

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

So, D is the correct option