Answer :
To simplify the expression [tex]\(\left(7x + 2 + 8x^4\right) - \left(2x - 5 - 8x^4\right) + \left(3x + 5x^4\right)\)[/tex], we can break it down step-by-step by combining like terms:
1. Distribute and combine similar expressions:
- Start with the expression:
[tex]\[
(7x + 2 + 8x^4) - (2x - 5 - 8x^4) + (3x + 5x^4)
\][/tex]
- Distribute the negative sign in the second term:
[tex]\[
= 7x + 2 + 8x^4 - 2x + 5 + 8x^4 + 3x + 5x^4
\][/tex]
2. Combine like terms for each power of [tex]\(x\)[/tex]:
- [tex]\(x^4\)[/tex] terms: [tex]\(8x^4 + 8x^4 + 5x^4 = 21x^4\)[/tex]
- [tex]\(x\)[/tex] terms: [tex]\(7x - 2x + 3x = 8x\)[/tex]
- Constant terms: [tex]\(2 + 5 = 7\)[/tex]
3. Write the simplified expression:
- The simplified expression is:
[tex]\[
21x^4 + 8x + 7
\][/tex]
Therefore, the correct answer is [tex]\(\boxed{21x^4 + 8x + 7}\)[/tex], which matches option C) from the given choices.
1. Distribute and combine similar expressions:
- Start with the expression:
[tex]\[
(7x + 2 + 8x^4) - (2x - 5 - 8x^4) + (3x + 5x^4)
\][/tex]
- Distribute the negative sign in the second term:
[tex]\[
= 7x + 2 + 8x^4 - 2x + 5 + 8x^4 + 3x + 5x^4
\][/tex]
2. Combine like terms for each power of [tex]\(x\)[/tex]:
- [tex]\(x^4\)[/tex] terms: [tex]\(8x^4 + 8x^4 + 5x^4 = 21x^4\)[/tex]
- [tex]\(x\)[/tex] terms: [tex]\(7x - 2x + 3x = 8x\)[/tex]
- Constant terms: [tex]\(2 + 5 = 7\)[/tex]
3. Write the simplified expression:
- The simplified expression is:
[tex]\[
21x^4 + 8x + 7
\][/tex]
Therefore, the correct answer is [tex]\(\boxed{21x^4 + 8x + 7}\)[/tex], which matches option C) from the given choices.
