Answer :
Sure! Let's simplify the expression [tex]\((5x^3 - 5x - 8) + (2x^3 + 4x + 2)\)[/tex] step by step.
1. Identify and combine like terms:
We have two expressions here. We'll combine the terms based on their power of [tex]\(x\)[/tex].
- For the [tex]\(x^3\)[/tex] terms:
- From the first expression, we have [tex]\(5x^3\)[/tex].
- From the second expression, we have [tex]\(2x^3\)[/tex].
- Adding these gives us [tex]\(5x^3 + 2x^3 = 7x^3\)[/tex].
- For the [tex]\(x\)[/tex] terms:
- From the first expression, we have [tex]\(-5x\)[/tex].
- From the second expression, we have [tex]\(4x\)[/tex].
- Adding these gives us [tex]\(-5x + 4x = -1x\)[/tex].
- For the constant terms:
- From the first expression, we have [tex]\(-8\)[/tex].
- From the second expression, we have [tex]\(2\)[/tex].
- Adding these gives us [tex]\(-8 + 2 = -6\)[/tex].
2. Write the simplified expression:
Combine all the simplified terms to get the final expression:
[tex]\[
7x^3 - 1x - 6
\][/tex]
3. Choose the correct simplification from the options given:
Comparing with the options, the correct simplification is:
[tex]\[
7x^3 - x - 6
\][/tex]
Therefore, the correct answer is: [tex]\(7x^3 - x - 6\)[/tex].
1. Identify and combine like terms:
We have two expressions here. We'll combine the terms based on their power of [tex]\(x\)[/tex].
- For the [tex]\(x^3\)[/tex] terms:
- From the first expression, we have [tex]\(5x^3\)[/tex].
- From the second expression, we have [tex]\(2x^3\)[/tex].
- Adding these gives us [tex]\(5x^3 + 2x^3 = 7x^3\)[/tex].
- For the [tex]\(x\)[/tex] terms:
- From the first expression, we have [tex]\(-5x\)[/tex].
- From the second expression, we have [tex]\(4x\)[/tex].
- Adding these gives us [tex]\(-5x + 4x = -1x\)[/tex].
- For the constant terms:
- From the first expression, we have [tex]\(-8\)[/tex].
- From the second expression, we have [tex]\(2\)[/tex].
- Adding these gives us [tex]\(-8 + 2 = -6\)[/tex].
2. Write the simplified expression:
Combine all the simplified terms to get the final expression:
[tex]\[
7x^3 - 1x - 6
\][/tex]
3. Choose the correct simplification from the options given:
Comparing with the options, the correct simplification is:
[tex]\[
7x^3 - x - 6
\][/tex]
Therefore, the correct answer is: [tex]\(7x^3 - x - 6\)[/tex].
