25. \( \left(8 c^{9} d^{5}\right)\left(4 c^{2} d^{3}\right)-\left(19 c^{10} d\right)\left(c d^{7}\right) \)

To simplify \( \left(8 c^{9} d^{5}\right)\left(4 c^{2} d^{3}\right)-\left(19 c^{10} d\right)\left(c d^{7}\right) \), let's break it down step by step. First, we simplify the first term: \[ \left(8 c^9 d^5\right)\left(4 c^2 d^3\right) = 8 \cdot 4 \cdot c^{9+2} \cdot d^{5+3} = 32 c^{11} d^{8} \] Now for the second term: \[ \left(19 c^{10} d\right)\left(c d^{7}\right) = 19 \cdot c^{10+1} \cdot d^{1+7} = 19 c^{11} d^{8} \] Now we can subtract the two terms: \[ 32 c^{11} d^{8} - 19 c^{11} d^{8} \] Since both terms have the same base \( c^{11} d^{8} \), we can combine them: \[ (32 - 19) c^{11} d^{8} = 13 c^{11} d^{8} \] Thus, the simplified expression is: \[ \boxed{13 c^{11} d^{8}} \]