Multiply.
-$\left(x+\frac{1}{3}\right)\left(2 x^{3}+4 x^{2}-4 x-4\right)$
A) $2 x^{4}+\frac{14}{3} x^{3}-\frac{8}{3} x^{2}-\frac{16}{3} x-\frac{4}{3}$
B) $2 x^{4}+\frac{14}{3} x^{3}+\frac{16}{3} x^{2}+\frac{16}{3} x-\frac{4}{3}$
C) $2 x^{4}+\frac{14}{3} x^{3}+\frac{16}{3} x^{2}-\frac{16}{3} x-\frac{4}{3}$
D) $2 x^{4}-\frac{14}{3} x^{3}+\frac{8}{3} x^{2}-\frac{16}{3} x+\frac{4}{3}$

Question

Quizplus · Accepted Answer

To multiply $\left(x+\frac{1}{3}\right)\left(2 x^{3}+4 x^{2}-4 x-4\right)$, distribute each term in the first polynomial across the second polynomial:- $x \cdot 2x^3 = 2x^4$- $x \cdot 4x^2 = 4x^3$- $x \cdot (-4x) = -4x^2$- $x \cdot (-4) = -4x$- $\frac{1}{3} \cdot 2x^3 = \frac{2}{3}x^3$- $\frac{1}{3} \cdot 4x^2 = \frac{4}{3}x^2$- $\frac{1}{3} \cdot (-4x) = -\frac{4}{3}x$- $\frac{1}{3} \cdot (-4) = -\frac{4}{3}$Adding these results together:- $2x^4 + (4x^3 + \frac{2}{3}x^3) + (-4x^2 + \frac{4}{3}x^2) + (-4x - \frac{4}{3}x) - \frac{4}{3}$- Simplify to get $2x^4 + \frac{14}{3}x^3 - \frac{8}{3}x^2 - \frac{16}{3}x - \frac{4}{3}$Therefore, the correct answer is A) $2 x^{4}+\frac{14}{3} x^{3}-\frac{8}{3} x^{2}-\frac{16}{3} x-\frac{4}{3}$.

Multiply - (x+13)(2x3+4x2−4x−4)\left(x+\frac{1}{3}\right)\left(2 x^{3}+4 x^{2}-4 x-4\right)(x+31​)(2x3+4x2−4x−4) A) 2x4+143x3−83x2−163x−432 x^{4}+\frac{14}{3} x^{3}-\frac{8}{3} x^{2}-\frac{16}{3} x-\frac{4}{3}2x4+314​x3−38​x2−316​x−34​

Multiply
- $\left(x+\frac{1}{3}\right)\left(2 x^{3}+4 x^{2}-4 x-4\right)$ A) $2 x^{4}+\frac{14}{3} x^{3}-\frac{8}{3} x^{2}-\frac{16}{3} x-\frac{4}{3}$