determine which expression when simplified will result in the following polynomial.
$4x^3 + 6x^2 - 8x + 4$
a. $(8x^3 + 5x^2 + 6x + 1) - (12x^3 - x^2 - 2x - 3)$
b. $(8x^3 - 2x^2 - 6x - 1) - (12x^3 - 4x^2 + 2x + 3)$
c. $(8x^3 + 2x^2 + 4x - 2) - (4x^3 - 4x^2 - 4x + 2)$
d. $(8x^3 + 5x^2 - 6x + 1) - (4x^3 - x^2 + 2x - 3)$

Question

Accepted Answer

# Answer:
D. $(8x^{3}+5x^{2}-6x + 1)-(4x^{3}-x^{2}+2x - 3)$
# Explanation:
## Step1: Simplify Option A
$$
\begin{align*}
&(8x^{3}+5x^{2}+6x + 1)-(12x^{3}-x^{2}-2x - 3)\
=&8x^{3}+5x^{2}+6x + 1 - 12x^{3}+x^{2}+2x + 3\
=&(8x^{3}-12x^{3})+(5x^{2}+x^{2})+(6x + 2x)+(1 + 3)\
=& - 4x^{3}+6x^{2}+8x + 4
\end{align*}
$$
Not equal to $4x^{3}+6x^{2}-8x + 4$.

## Step2: Simplify Option B
$$
\begin{align*}
&(8x^{3}-2x^{2}-6x - 1)-(12x^{3}-4x^{2}+2x + 3)\
=&8x^{3}-2x^{2}-6x - 1 - 12x^{3}+4x^{2}-2x - 3\
=&(8x^{3}-12x^{3})+(-2x^{2}+4x^{2})+(-6x - 2x)+(-1 - 3)\
=& - 4x^{3}+2x^{2}-8x - 4
\end{align*}
$$
Not equal to $4x^{3}+6x^{2}-8x + 4$.

## Step3: Simplify Option C
$$
\begin{align*}
&(8x^{3}+2x^{2}+4x - 2)-(4x^{3}-4x^{2}-4x + 2)\
=&8x^{3}+2x^{2}+4x - 2 - 4x^{3}+4x^{2}+4x - 2\
=&(8x^{3}-4x^{3})+(2x^{2}+4x^{2})+(4x + 4x)+(-2 - 2)\
=&4x^{3}+6x^{2}+8x - 4
\end{align*}
$$
Not equal to $4x^{3}+6x^{2}-8x + 4$.

## Step4: Simplify Option D
$$
\begin{align*}
&(8x^{3}+5x^{2}-6x + 1)-(4x^{3}-x^{2}+2x - 3)\
=&8x^{3}+5x^{2}-6x + 1 - 4x^{3}+x^{2}-2x + 3\
=&(8x^{3}-4x^{3})+(5x^{2}+x^{2})+(-6x - 2x)+(1 + 3)\
=&4x^{3}+6x^{2}-8x + 4
\end{align*}
$$
Which matches the given polynomial.

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QUESTION IMAGE

Question

Explanation:

Step1: Simplify Option A

Step2: Simplify Option B

Step3: Simplify Option C

Step4: Simplify Option D

Answer: