Simplify the following expression:

[tex]\( 2x^5 + 3x^3 - 5x^2 + x^2 + 7x + 1 + 7x^5 - 3x^3 - 4 \)[/tex]

A. [tex]\( 5x^5 + 5x^2 + 7x - 3 \)[/tex]
B. [tex]\( 9x^5 - 4x^2 + 7x + 5 \)[/tex]
C. [tex]\( 9x^5 + 6x^2 + 7x + 3 \)[/tex]
D. [tex]\( 9x^5 - 4x^2 + 7x - 3 \)[/tex]



Answer :

To simplify the expression [tex]\(2x^5 + 3x^3 - 5x^2 + x^2 + 7x + 1 + 7x^5 - 3x^3 - 4\)[/tex], we follow these steps:

1. Identify and Combine Like Terms:
- Terms with [tex]\(x^5\)[/tex]:
[tex]\[ 2x^5 + 7x^5 = 9x^5 \][/tex]
- Terms with [tex]\(x^3\)[/tex]:
[tex]\[ 3x^3 - 3x^3 = 0 \][/tex]
These terms cancel each other out.
- Terms with [tex]\(x^2\)[/tex]:
[tex]\[ -5x^2 + x^2 = -4x^2 \][/tex]
- Terms with [tex]\(x\)[/tex]:
[tex]\[ 7x \][/tex]
There are no other [tex]\(x\)[/tex] terms to combine with.
- Constant terms:
[tex]\[ 1 - 4 = -3 \][/tex]

2. Combine all the simplified terms:
[tex]\[ 9x^5 - 4x^2 + 7x - 3 \][/tex]

Hence, the simplified form of the given expression is:

[tex]\[ 9x^5 - 4x^2 + 7x - 3 \][/tex]

Therefore, the correct answer is:

D. [tex]\(9x^5 - 4x^2 + 7x - 3\)[/tex]