Question

simplify the following expression.
$(2x - 5)(6x^{2} - 6x - 11)$
a. $12x^{3}-42x^{2}+8x - 55$
b. $12x^{3}-18x^{2}-52x + 55$
c. $12x^{3}+18x^{2}-52x - 55$
d. $12x^{3}-42x^{2}+8x + 55$

Explanation:

Step1: Distribute 2x to each term

$2x \cdot 6x^2 + 2x \cdot (-6x) + 2x \cdot (-11)$
$= 12x^3 - 12x^2 - 22x$

Step2: Distribute -5 to each term

$-5 \cdot 6x^2 + (-5) \cdot (-6x) + (-5) \cdot (-11)$
$= -30x^2 + 30x + 55$

Step3: Combine all expanded terms

$12x^3 - 12x^2 - 22x - 30x^2 + 30x + 55$

Step4: Combine like terms

$12x^3 + (-12x^2 - 30x^2) + (-22x + 30x) + 55$
$= 12x^3 - 42x^2 + 8x + 55$

Answer:

D. $12x^3 - 42x^2 + 8x + 55$