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------------------------------------------------ Question 3 of 25

Which expression is the simplest form of [tex]$3x^3 + x^2 + 2(x^3 - 4x^2)$[/tex]?

A. [tex]$5x^3 - 3x^2$[/tex]
B. [tex][tex]$x^3 - 9x^2$[/tex][/tex]
C. [tex]$5x^3 - 7x^2$[/tex]
D. [tex]$2x^3 - 8x^2$[/tex]

To simplify the given expression [tex]$3x^3 + x^2 + 2(x^3 - 4x^2)$[/tex], let's proceed step-by-step:

1. Distribute the 2 inside the parentheses:
[tex]\[
3x^3 + x^2 + 2(x^3 - 4x^2) = 3x^3 + x^2 + 2x^3 - 8x^2
\][/tex]

2. Combine like terms:
- First, combine the [tex]$x^3$[/tex] terms:
[tex]\[
3x^3 + 2x^3 = 5x^3
\][/tex]
- Next, combine the [tex]$x^2$[/tex] terms:
[tex]\[
x^2 - 8x^2 = -7x^2
\][/tex]

3. Put it all together:
[tex]\[
3x^3 + x^2 + 2x^3 - 8x^2 = 5x^3 - 7x^2
\][/tex]

So, the simplest form of the expression is:
[tex]\[
5x^3 - 7x^2
\][/tex]

Therefore, the correct answer is:
C. [tex]$5x^3 - 7x^2$[/tex]