Question

what is the simplest form of this expression? -(x - 2)(3x^2 + 4x - 5)

a. -3x^3 + 2x^2 + 13x - 10
b. 3x^3 - 10x^2 - 3x - 10
c. 3x^3 - 2x^2 - 13x + 10
d. -3x^3 - 10x^2 - 3x + 10

Explanation:

Step1: Apply distributive property

First, distribute the negative sign to \((x - 2)\) to get \((-x + 2)(3x^{2}+4x - 5)\).

Step2: Multiply each term

\[

$$\begin{align*} (-x)\times(3x^{2}+4x - 5)+2\times(3x^{2}+4x - 5)&=(-x)\times3x^{2}+(-x)\times4x+(-x)\times(- 5)+2\times3x^{2}+2\times4x+2\times(-5)\\ &=-3x^{3}-4x^{2}+5x + 6x^{2}+8x-10 \end{align*}$$

\]

Step3: Combine like - terms

\[

$$\begin{align*} -3x^{3}+(-4x^{2}+6x^{2})+(5x + 8x)-10&=-3x^{3}+2x^{2}+13x-10 \end{align*}$$

\]

Answer:

A. \(-3x^{3}+2x^{2}+13x - 10\)