To find the difference between the given polynomials, we first need to simplify each expression individually.
1. **First Polynomial**: 5x³ + 4x² + 6x² + 2x + 9
- Combine like terms:
- 4x² + 6x² = 10x²
This gives us:
- 5x³ + 10x² + 2x + 9
2. **Second Polynomial**: x³ + 6x² + 9 + x³ + 2x² + 5x³ + 2x² + 2x + 9 + 5x³ + 2x² + 2x + 9
- Combine all the terms:
- Collect x³ terms: 1 + 1 + 5 = 7x³
- Collect x² terms: 6 + 2 + 2 + 2 = 12x²
- Collect x terms: 2 + 2 + 2 = 6x
- Combine constant terms: 9 + 9 + 9 = 27
This yields:
- 7x³ + 12x² + 6x + 27
Now, we can find the difference between the simplified versions of the two polynomials:
- (5x³ + 10x² + 2x + 9) – (7x³ + 12x² + 6x + 27)
We subtract the coefficients of like terms:
- For x³: 5 – 7 = -2x³
- For x²: 10 – 12 = -2x²
- For x: 2 – 6 = -4x
- For constant terms: 9 – 27 = -18
Putting it all together, the difference of the polynomials is:
- -2x³ – 2x² – 4x – 18
This is the final result for the difference between the two polynomials.