Let's simplify each expression step-by-step.
### Expression 1: [tex]\(3x^3 + 8x^2 - 2x^4 - 3x^2 + 5x^3 - x\)[/tex]
1. Combine like terms:
- [tex]\(3x^3 + 5x^3\)[/tex] gives [tex]\(8x^3\)[/tex]
- [tex]\(8x^2 - 3x^2\)[/tex] gives [tex]\(5x^2\)[/tex]
- There are no like terms for [tex]\(-2x^4\)[/tex] and [tex]\(-x\)[/tex]
2. The simplified expression is:
[tex]\[ -2x^4 + 8x^3 + 5x^2 - x \][/tex]
### Expression 2: [tex]\(2x^4 + 5x^3 + 8x^2 + x\)[/tex]
1. All terms are unique and cannot be combined with others:
[tex]\[ 2x^4 + 5x^3 + 8x^2 + x \][/tex]
### Expression 3: [tex]\(10x\)[/tex]
1. This expression is already simplified as there are no like terms to combine:
[tex]\[ 10x \][/tex]
### Expression 4: [tex]\(-2x^4 + 8x^3 + 5x^2 - x\)[/tex]
1. This expression is already simplified as there are no like terms to combine:
[tex]\[ -2x^4 + 8x^3 + 5x^2 - x \][/tex]
### Expression 5: [tex]\(10x^4\)[/tex]
1. This expression is already simplified as there are no like terms to combine:
[tex]\[ 10x^4 \][/tex]
### Summary
The simplified versions of the expressions are:
1. [tex]\( -2x^4 + 8x^3 + 5x^2 - x \)[/tex]
2. [tex]\( 2x^4 + 5x^3 + 8x^2 + x \)[/tex]
3. [tex]\( 10x \)[/tex]
4. [tex]\( -2x^4 + 8x^3 + 5x^2 - x \)[/tex]
5. [tex]\( 10x^4 \)[/tex]
