Answer: Yes, the degree of sum is differ from the degree of difference.
Step-by-step explanation:
Degree of a polynomial is a highest power of its monomials ( single term).
Here, the given polynomials are,
![x^7+3x^5+3x+1](https://tex.z-dn.net/?f=x%5E7%2B3x%5E5%2B3x%2B1)
![x^7+5x+10](https://tex.z-dn.net/?f=x%5E7%2B5x%2B10)
By adding these two polynomials,
![x^7+3x^5+3x+1+x^7+5x+10](https://tex.z-dn.net/?f=x%5E7%2B3x%5E5%2B3x%2B1%2Bx%5E7%2B5x%2B10)
![=2x^7+3x^5+8x+11](https://tex.z-dn.net/?f=%3D2x%5E7%2B3x%5E5%2B8x%2B11)
Since, the highest power of x in this result = 7
Hence, the degree of sum of the given polynomials = 7
Now, by subtracting the given polynomials,
![(x^7+3x^5+3x+1)-(x^7+5x+10](https://tex.z-dn.net/?f=%28x%5E7%2B3x%5E5%2B3x%2B1%29-%28x%5E7%2B5x%2B10)
![=x^7+3x^5+3x+1-x^7-5x-10](https://tex.z-dn.net/?f=%3Dx%5E7%2B3x%5E5%2B3x%2B1-x%5E7-5x-10)
![=3x^5-2x-9](https://tex.z-dn.net/?f=%3D3x%5E5-2x-9)
Since, the highest power of x in this result = 5,
Hence, the degree of difference of the given polynomials = 5
Thus, both the degree of sum and difference are different.