35. \( \frac{(t-3)^{3}\left(t^{2}-2 t+1\right)}{(t-1)^{3}\left(t^{2}-4 t+4\right)} \)

To simplify the expression \( \frac{(t-3)^{3}(t^{2}-2t+1)}{(t-1)^{3}(t^{2}-4t+4)} \), we first recognize that \( t^{2}-2t+1 \) and \( t^{2}-4t+4 \) can be factored: 1. \( t^{2}-2t+1 = (t-1)^{2} \) 2. \( t^{2}-4t+4 = (t-2)^{2} \) Now we can rewrite the original expression: \[ \frac{(t-3)^{3}((t-1)^{2})}{(t-1)^{3}((t-2)^{2})} \] Next, we can simplify by cancelling the common factors: \[ = \frac{(t-3)^{3}}{(t-1)^{1}(t-2)^{2}} \] Thus, the simplified form of the expression is: \[ \frac{(t-3)^{3}}{(t-1)(t-2)^{2}} \]