Question

select the correct answer from each drop - down menu. consider the expressions given below. a. (2x^{3}-x^{2}-6x) b. (2x^{3}+8x + 4) c. (3x^{4}+x^{2}+x - 7) d. (3x^{4}-3x^{2}+5x - 7) for each expression below, select the letter that corresponds to the equivalent expression from the given list. ((4x^{3}-4 + 7x)-(2x^{3}-x - 8)) is equivalent to expression ((-3x^{2}+x^{4}+x)+(2x^{4}-7 + 4x)) is equivalent to expression ((x^{2}-2x)(2x + 3)) is equivalent to expression

Explanation:

Step1: Simplify the first expression

\[

$$\begin{align*} &(4x^{3}-4 + 7x)-(2x^{3}-x - 8)\\ =&4x^{3}-4 + 7x-2x^{3}+x + 8\\ =&(4x^{3}-2x^{3})+(7x+x)+(-4 + 8)\\ =&2x^{3}+8x + 4 \end{align*}$$

\]
This is equivalent to expression B.

Step2: Simplify the second expression

\[

$$\begin{align*} &(-3x^{2}+x^{4}+x)+(2x^{4}-7 + 4x)\\ =&(-3x^{2})+(x^{4}+2x^{4})+(x + 4x)-7\\ =&3x^{4}-3x^{2}+5x-7 \end{align*}$$

\]
This is equivalent to expression D.

Step3: Simplify the third expression

\[

$$\begin{align*} &(x^{2}-2x)(2x + 3)\\ =&x^{2}(2x+3)-2x(2x + 3)\\ =&2x^{3}+3x^{2}-4x^{2}-6x\\ =&2x^{3}-x^{2}-6x \end{align*}$$

\]
This is equivalent to expression A.

Answer:

First expression: B. \(2x^{3}+8x + 4\)
Second expression: D. \(3x^{4}-3x^{2}+5x-7\)
Third expression: A. \(2x^{3}-x^{2}-6x\)