Answer :
Sure, let's simplify each of the polynomials step by step:
1. Polynomial: [tex]\( 20x^8 + 15x^4 + 35x^4 \)[/tex]
- Combine like terms:
[tex]\[
15x^4 + 35x^4 = 50x^4
\][/tex]
- Simplified polynomial:
[tex]\[
20x^8 + 50x^4
\][/tex]
2. Polynomial: [tex]\( 6x^3 - 16x^2 - 38x + 24 \)[/tex]
- This polynomial has no like terms, so it is already simplified.
3. Polynomial: [tex]\( 10x^2 + 20x - 4 \)[/tex]
- This polynomial has no like terms, so it is already simplified.
4. Polynomial: [tex]\( 20x^6 + 15x^5 + 35x^4 \)[/tex]
- This polynomial has no like terms, so it is already simplified.
5. Polynomial: [tex]\( 9x^2 + 49 \)[/tex]
- This polynomial has no like terms, so it is already simplified.
6. Polynomial: [tex]\( 9x^2 + 42x - 49 \)[/tex]
- This polynomial has no like terms, so it is already simplified.
7. Polynomial: [tex]\( 6x^2 + 16x + 24 \)[/tex]
- This polynomial has no like terms, so it is already simplified.
8. Polynomial: [tex]\( x^2 - 81 \)[/tex]
- This polynomial has no like terms, so it is already simplified.
9. Polynomial: [tex]\( 25x^2 - 20x + 4 \)[/tex]
- This polynomial has no like terms, so it is already simplified.
10. Polynomial: [tex]\( 9x^2 - 49 \)[/tex]
- This polynomial has no like terms, so it is already simplified.
11. Polynomial: [tex]\( x^2 + 81 \)[/tex]
- This polynomial has no like terms, so it is already simplified.
12. Polynomial: [tex]\( x^2 + 18x - 81 \)[/tex]
- This polynomial has no like terms, so it is already simplified.
Here are the simplified versions of each polynomial individually evaluated.
1. Polynomial: [tex]\( 20x^8 + 15x^4 + 35x^4 \)[/tex]
- Combine like terms:
[tex]\[
15x^4 + 35x^4 = 50x^4
\][/tex]
- Simplified polynomial:
[tex]\[
20x^8 + 50x^4
\][/tex]
2. Polynomial: [tex]\( 6x^3 - 16x^2 - 38x + 24 \)[/tex]
- This polynomial has no like terms, so it is already simplified.
3. Polynomial: [tex]\( 10x^2 + 20x - 4 \)[/tex]
- This polynomial has no like terms, so it is already simplified.
4. Polynomial: [tex]\( 20x^6 + 15x^5 + 35x^4 \)[/tex]
- This polynomial has no like terms, so it is already simplified.
5. Polynomial: [tex]\( 9x^2 + 49 \)[/tex]
- This polynomial has no like terms, so it is already simplified.
6. Polynomial: [tex]\( 9x^2 + 42x - 49 \)[/tex]
- This polynomial has no like terms, so it is already simplified.
7. Polynomial: [tex]\( 6x^2 + 16x + 24 \)[/tex]
- This polynomial has no like terms, so it is already simplified.
8. Polynomial: [tex]\( x^2 - 81 \)[/tex]
- This polynomial has no like terms, so it is already simplified.
9. Polynomial: [tex]\( 25x^2 - 20x + 4 \)[/tex]
- This polynomial has no like terms, so it is already simplified.
10. Polynomial: [tex]\( 9x^2 - 49 \)[/tex]
- This polynomial has no like terms, so it is already simplified.
11. Polynomial: [tex]\( x^2 + 81 \)[/tex]
- This polynomial has no like terms, so it is already simplified.
12. Polynomial: [tex]\( x^2 + 18x - 81 \)[/tex]
- This polynomial has no like terms, so it is already simplified.
Here are the simplified versions of each polynomial individually evaluated.
