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. $3x^{4}-3x^{3}+5x - 7$
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 first expression

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

Step2: Simplify second expression

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

Step3: Simplify third expression

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

Answer:

1. $(4x^3 - 4 + 7x) - (2x^3 - x - 8)$ is equivalent to expression B. $2x^3 + 8x + 4$
2. $(-3x^2 + x^4 + x) + (2x^4 - 7 + 4x)$ is equivalent to expression D. $3x^4 - 3x^2 + 5x - 7$
3. $(x^2 - 2x)(2x + 3)$ is equivalent to expression A. $2x^3 - x^2 - 6x$