Write the degree of each polynomials given below :
`x^(5)y^(7) - 8x^(3)y^(8) + 10x^(4)y^(4)z^(4)`

Answer

To find the degree of the polynomial \( x^{5}y^{7} - 8x^{3}y^{8} + 10x^{4}y^{4}z^{4} \), we will analyze each term separately and then determine the highest degree among them.

### Step-by-Step Solution:

1. **Identify the Terms:**
The polynomial consists of three terms:
- \( x^{5}y^{7} \)
- \( -8x^{3}y^{8} \)
- \( 10x^{4}y^{4}z^{4} \)

2. **Calculate the Degree of Each Term:**
- **First Term: \( x^{5}y^{7} \)**
- The degree is calculated by adding the exponents of \( x \) and \( y \):
\[ \text{Degree} = 5 + 7 = 12 \]

- **Second Term: \( -8x^{3}y^{8} \)**
- The degree is calculated similarly:
\[ \text{Degree} = 3 + 8 = 11 \]

- **Third Term: \( 10x^{4}y^{4}z^{4} \)**
- Here, we add the exponents of \( x \), \( y \), and \( z \):
\[ \text{Degree} = 4 + 4 + 4 = 12 \]

3. **Determine the Highest Degree:**
Now, we compare the degrees of all three terms:
- Degree of \( x^{5}y^{7} = 12 \)
- Degree of \( -8x^{3}y^{8} = 11 \)
- Degree of \( 10x^{4}y^{4}z^{4} = 12 \)

The highest degree among these is \( 12 \).

4. **Conclusion:**
Therefore, the degree of the polynomial \( x^{5}y^{7} - 8x^{3}y^{8} + 10x^{4}y^{4}z^{4} \) is:
\[ \text{Degree} = 12 \]