High School

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Simplify: [tex]\left(7x^3 - 2x^2\right) + \left(x^3 + 9 + 3x^2\right)[/tex]

A. [tex]6x^3 + 7x^2 + 9[/tex]

B. [tex]6x^3 + x^2 + 9[/tex]

C. [tex]8x^3 - x^2 + 9[/tex]

D. [tex]8x^3 + x^2 + 9[/tex]

Answer :

Sure! Let's simplify the expression step-by-step:

We have two expressions to combine:
1. [tex]\( 7x^3 - 2x^2 \)[/tex]
2. [tex]\( x^3 + 9 + 3x^2 \)[/tex]

Now, we'll add them together:

[tex]\[
(7x^3 - 2x^2) + (x^3 + 9 + 3x^2)
\][/tex]

We'll start by combining the like terms:

1. Combine the [tex]\(x^3\)[/tex] terms:
- [tex]\(7x^3 + x^3 = 8x^3\)[/tex]

2. Combine the [tex]\(x^2\)[/tex] terms:
- [tex]\(-2x^2 + 3x^2 = x^2\)[/tex]

3. The constant term is just 9, as there's no other constant term to combine it with.

So, combining all these, we get the simplified expression:

[tex]\[
8x^3 + x^2 + 9
\][/tex]

Therefore, the simplified expression is [tex]\(8x^3 + x^2 + 9\)[/tex]. The correct answer is option D:

D [tex]\(8x^3 + x^2 + 9\)[/tex]

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