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Answer :
To simplify the expression [tex]\((4x^3 + 6x - 7) + (3x^3 - 5x^2 - 5x + 9)\)[/tex], we need to combine like terms. Let's go through it step-by-step:
1. Identify like terms from both expressions:
- Cubic terms ([tex]\(x^3\)[/tex]): [tex]\(4x^3\)[/tex] and [tex]\(3x^3\)[/tex].
- Quadratic terms ([tex]\(x^2\)[/tex]): There is no [tex]\(x^2\)[/tex] term in the first expression, and the second expression has [tex]\(-5x^2\)[/tex].
- Linear terms ([tex]\(x\)[/tex]): [tex]\(6x\)[/tex] and [tex]\(-5x\)[/tex].
- Constant terms: [tex]\(-7\)[/tex] and [tex]\(9\)[/tex].
2. Combine like terms:
- Cubic terms: Add [tex]\(4x^3\)[/tex] and [tex]\(3x^3\)[/tex]:
[tex]\[
4x^3 + 3x^3 = 7x^3
\][/tex]
- Quadratic terms: Since there is no [tex]\(x^2\)[/tex] term in the first expression, we just take the term from the second expression:
[tex]\[
-5x^2
\][/tex]
- Linear terms: Add [tex]\(6x\)[/tex] and [tex]\(-5x\)[/tex]:
[tex]\[
6x - 5x = 1x
\][/tex]
- Constant terms: Add [tex]\(-7\)[/tex] and [tex]\(9\)[/tex]:
[tex]\[
-7 + 9 = 2
\][/tex]
3. Write the simplified expression by combining all the like terms:
[tex]\[
7x^3 - 5x^2 + x + 2
\][/tex]
Thus, the simplest form of the given expression is [tex]\(7x^3 - 5x^2 + x + 2\)[/tex].
The correct answer is:
A. [tex]\(7x^3 - 5x^2 + x + 2\)[/tex]
1. Identify like terms from both expressions:
- Cubic terms ([tex]\(x^3\)[/tex]): [tex]\(4x^3\)[/tex] and [tex]\(3x^3\)[/tex].
- Quadratic terms ([tex]\(x^2\)[/tex]): There is no [tex]\(x^2\)[/tex] term in the first expression, and the second expression has [tex]\(-5x^2\)[/tex].
- Linear terms ([tex]\(x\)[/tex]): [tex]\(6x\)[/tex] and [tex]\(-5x\)[/tex].
- Constant terms: [tex]\(-7\)[/tex] and [tex]\(9\)[/tex].
2. Combine like terms:
- Cubic terms: Add [tex]\(4x^3\)[/tex] and [tex]\(3x^3\)[/tex]:
[tex]\[
4x^3 + 3x^3 = 7x^3
\][/tex]
- Quadratic terms: Since there is no [tex]\(x^2\)[/tex] term in the first expression, we just take the term from the second expression:
[tex]\[
-5x^2
\][/tex]
- Linear terms: Add [tex]\(6x\)[/tex] and [tex]\(-5x\)[/tex]:
[tex]\[
6x - 5x = 1x
\][/tex]
- Constant terms: Add [tex]\(-7\)[/tex] and [tex]\(9\)[/tex]:
[tex]\[
-7 + 9 = 2
\][/tex]
3. Write the simplified expression by combining all the like terms:
[tex]\[
7x^3 - 5x^2 + x + 2
\][/tex]
Thus, the simplest form of the given expression is [tex]\(7x^3 - 5x^2 + x + 2\)[/tex].
The correct answer is:
A. [tex]\(7x^3 - 5x^2 + x + 2\)[/tex]
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