\(a,5\sqrt{25a^2}-25a\left(a< 0\right)=5\cdot\left|5a\right|-25a=-25a-25a=50a\\ b,\sqrt{49a^2}+3a\left(a>0\right)=\left|7a\right|+3a=10a\\ c,\sqrt{64a^2}-8a\left(a\in R\right)=\left|8a\right|-8a=\left[{}\begin{matrix}0,\forall a\ge0\\-16a,\forall a< 0\end{matrix}\right.\\ d,\sqrt{9a^6}-6a^3=\left|3a^3\right|-6a^3=\left[{}\begin{matrix}-3a^3,\forall a\ge0\\-9a^3,\forall a< 0\end{matrix}\right.\)