Question

which represents the following expression in simplest form?
$7(4x^3 - 6x) - (8x^2 - x + 10) + 2(3x^3 - 9x^2 - 1)$
a $6x^3 + 2x^2 - 41x - 12$
b $34x^2 - 26x^3 - 41x - 12$
c $34x^3 - 26x^2 - 43x + 8$
d $6x^3 - 17x^2 - 7x + 9$

Explanation:

Step1: Expand all parentheses

$7(4x^3-6x) = 28x^3 - 42x$
$-(8x^2-x+10) = -8x^2 + x - 10$
$2(3x^3-9x^2-1) = 6x^3 - 18x^2 - 2$

Step2: Combine all expanded terms

$28x^3 - 42x -8x^2 + x -10 +6x^3 -18x^2 -2$

Step3: Group like terms

$(28x^3 + 6x^3) + (-8x^2 -18x^2) + (-42x + x) + (-10 -2)$

Step4: Simplify each group

$34x^3 -26x^2 -41x -12$

Answer:

B. $34x^3-26x^2-41x-12$