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Answer :
Sure! To simplify the expression [tex]\(\left(5x^3 - 5x - 8\right) + \left(2x^3 + 4x + 2\right)\)[/tex], follow these steps:
1. Combine the like terms for [tex]\(x^3\)[/tex]:
- [tex]\(5x^3\)[/tex] from the first polynomial
- [tex]\(2x^3\)[/tex] from the second polynomial
When you add these together:
[tex]\[
5x^3 + 2x^3 = 7x^3
\][/tex]
2. Combine the like terms for [tex]\(x\)[/tex]:
- [tex]\(-5x\)[/tex] from the first polynomial
- [tex]\(4x\)[/tex] from the second polynomial
When you add these together:
[tex]\[
-5x + 4x = -1x \quad \text{(or simply } -x\text{)}
\][/tex]
3. Combine the constant terms:
- [tex]\(-8\)[/tex] from the first polynomial
- [tex]\(2\)[/tex] from the second polynomial
When you add these together:
[tex]\[
-8 + 2 = -6
\][/tex]
Putting it all together, the simplified form of the expression [tex]\(\left(5x^3 - 5x - 8\right) + \left(2x^3 + 4x + 2\right)\)[/tex] is:
[tex]\[
7x^3 - x - 6
\][/tex]
So, the correct answer is:
[tex]\[
\boxed{7x^3 - x - 6}
\][/tex]
1. Combine the like terms for [tex]\(x^3\)[/tex]:
- [tex]\(5x^3\)[/tex] from the first polynomial
- [tex]\(2x^3\)[/tex] from the second polynomial
When you add these together:
[tex]\[
5x^3 + 2x^3 = 7x^3
\][/tex]
2. Combine the like terms for [tex]\(x\)[/tex]:
- [tex]\(-5x\)[/tex] from the first polynomial
- [tex]\(4x\)[/tex] from the second polynomial
When you add these together:
[tex]\[
-5x + 4x = -1x \quad \text{(or simply } -x\text{)}
\][/tex]
3. Combine the constant terms:
- [tex]\(-8\)[/tex] from the first polynomial
- [tex]\(2\)[/tex] from the second polynomial
When you add these together:
[tex]\[
-8 + 2 = -6
\][/tex]
Putting it all together, the simplified form of the expression [tex]\(\left(5x^3 - 5x - 8\right) + \left(2x^3 + 4x + 2\right)\)[/tex] is:
[tex]\[
7x^3 - x - 6
\][/tex]
So, the correct answer is:
[tex]\[
\boxed{7x^3 - x - 6}
\][/tex]
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