To combine the like terms in the expression \( 10cd^2 + 8cd^2 - 9cd^2 - 9cd^2 \), we can first group the coefficients of the \( cd^2 \) terms:
\[ 10 + 8 - 9 - 9 \]
Now, let's perform the calculations step by step:
- \( 10 + 8 = 18 \)
- \( 18 - 9 = 9 \)
- \( 9 - 9 = 0 \)
Since the total of the coefficients is 0, the combined expression is:
\[ 0 \]
Therefore, the simplified form of the expression is \( 0 \).