Question

which expression is the simplest form of $2x^3 + x^2 + 3\left(x^3 - 4x^2\
ight)$? \LXI0 a. $x^3 - 13x^2$ \LXI1 b. $5x^3 - 3x^2$ \LXI2 c. $3x^3 - 12x^2$ \LXI3 d. $5x^3 - 11x^2$

Explanation:

Step1: Expand the parentheses

$2x^3 + x^2 + 3(x^3 - 4x^2) = 2x^3 + x^2 + 3x^3 - 12x^2$

Step2: Combine like $x^3$ terms

$2x^3 + 3x^3 + x^2 - 12x^2 = 5x^3 + x^2 - 12x^2$

Step3: Combine like $x^2$ terms

$5x^3 + (1 - 12)x^2 = 5x^3 - 11x^2$

Answer:

D. $5x^3 - 11x^2$