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Answer :
Let's simplify the expression [tex]\(3x^3 - x^2 + 2(x^3 - 4x^2)\)[/tex] step by step.
1. Start with the given expression:
[tex]\[
3x^3 - x^2 + 2(x^3 - 4x^2)
\][/tex]
2. Distribute the 2 inside the parentheses:
[tex]\[
3x^3 - x^2 + 2x^3 - 8x^2
\][/tex]
3. Combine like terms by adding the coefficients of [tex]\(x^3\)[/tex] and [tex]\(x^2\)[/tex]:
- The [tex]\(x^3\)[/tex] terms: [tex]\(3x^3 + 2x^3 = 5x^3\)[/tex]
- The [tex]\(x^2\)[/tex] terms: [tex]\(-x^2 - 8x^2 = -9x^2\)[/tex]
4. So, combining these, we get:
[tex]\[
5x^3 - 9x^2
\][/tex]
Therefore, the simplest form of the expression [tex]\(3x^3 - x^2 + 2(x^3 - 4x^2)\)[/tex] is:
[tex]\[
\boxed{5x^3 - 9x^2}
\][/tex]
So, the correct answer is:
[tex]\[
\boxed{A. 5x^3 - 9x^2}
\][/tex]
1. Start with the given expression:
[tex]\[
3x^3 - x^2 + 2(x^3 - 4x^2)
\][/tex]
2. Distribute the 2 inside the parentheses:
[tex]\[
3x^3 - x^2 + 2x^3 - 8x^2
\][/tex]
3. Combine like terms by adding the coefficients of [tex]\(x^3\)[/tex] and [tex]\(x^2\)[/tex]:
- The [tex]\(x^3\)[/tex] terms: [tex]\(3x^3 + 2x^3 = 5x^3\)[/tex]
- The [tex]\(x^2\)[/tex] terms: [tex]\(-x^2 - 8x^2 = -9x^2\)[/tex]
4. So, combining these, we get:
[tex]\[
5x^3 - 9x^2
\][/tex]
Therefore, the simplest form of the expression [tex]\(3x^3 - x^2 + 2(x^3 - 4x^2)\)[/tex] is:
[tex]\[
\boxed{5x^3 - 9x^2}
\][/tex]
So, the correct answer is:
[tex]\[
\boxed{A. 5x^3 - 9x^2}
\][/tex]
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