Question

1. what is ((5x - 1)(8x^2 - 3x - 6))?

a. (40x^3 - 37x^2 + 6x)

b. (39x^3 - 23x^2 - 27x - 6)

c. (40x^3 - 38x^2 + 7x)

d. (40x^3 - 23x^2 - 27x + 6)

Explanation:

Step1: Distribute $5x$ to each term

$5x \cdot 8x^2 - 5x \cdot 3x - 5x \cdot 6$
$= 40x^3 - 15x^2 - 30x$

Step2: Distribute $-1$ to each term

$-1 \cdot 8x^2 + 1 \cdot 3x + 1 \cdot 6$
$= -8x^2 + 3x + 6$

Step3: Combine all resulting terms

$40x^3 - 15x^2 - 30x -8x^2 + 3x + 6$

Step4: Combine like terms

$40x^3 + (-15x^2-8x^2) + (-30x+3x) + 6$
$= 40x^3 -23x^2 -27x +6$

Answer:

d. $40x^{3}-23x^{2}-27x+6$