Question

(-2x² + 4x + 4)(3x - 5)?
x³ + 22x² - 8x - 20
-6x³ + 2x² - 8x - 5
-6x³ + 12x² + 15x - 5
-6x³ + 22x² + 32x - 2

Explanation:

Step1: Distribute $-2x^2$ to $(3x-5)$

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

Step2: Distribute $4x$ to $(3x-5)$

$$\begin{align*} 4x \cdot 3x + 4x \cdot (-5) &= 12x^2 - 20x \end{align*}$$

Step3: Distribute $4$ to $(3x-5)$

$$\begin{align*} 4 \cdot 3x + 4 \cdot (-5) &= 12x - 20 \end{align*}$$

Step4: Combine all terms

$$\begin{align*} -6x^3 + 10x^2 + 12x^2 - 20x + 12x - 20 &= -6x^3 + (10x^2+12x^2) + (-20x+12x) -20 \\ &= -6x^3 +22x^2 -8x -20 \end{align*}$$

Answer:

A. $-6x^3 + 22x^2 - 8x - 20$