Simplify \[ \begin{array}{l}\left.\text { 1. }-1 x^{3}+3 x-1 x^{2}+3\right)(1 x) \\ \text { 2. }-1 x^{3}+9 x^{2}+3 x \\ \text { 3. } 1 x^{3}+9 x^{2}+3 x \\ \text { 4. }-1 x^{3}+9 x^{2} \\ \text { 5. }-1 x^{2}+9 x+3\end{array} \]

Let's tackle the expression step by step! 1. **First expression: \((-1 x^{3}+3 x-1 x^{2}+3)(1 x)\)** Here, we need to distribute \(1x\) to each term inside the parentheses. \[ = -1 x^{3} \cdot 1 x + 3 x \cdot 1 x - 1 x^{2} \cdot 1 x + 3 \cdot 1 x \] \[ = -1 x^{4} + 3 x^{2} - 1 x^{3} + 3 x \] Now we can rearrange the terms: \[ = -1 x^{4} - 1 x^{3} + 3 x^{2} + 3 x \] 2. **Second expression: \(-1 x^{3}+9 x^{2}+3 x\)** This expression is already simplified. 3. **Third expression: \(1 x^{3}+9 x^{2}+3 x\)** Similar to the second expression, this one is also already simplified. 4. **Fourth expression: \(-1 x^{3}+9 x^{2}\)** This is simplified, representing a polynomial of degree 2. 5. **Fifth expression: \(-1 x^{2}+9 x+3\)** This expression is also fully simplified. In summary, the simplified expressions are: - \(-1 x^{4} - 1 x^{3} + 3 x^{2} + 3 x\) - \(-1 x^{3} + 9 x^{2} + 3 x\) - \(1 x^{3} + 9 x^{2} + 3 x\) - \(-1 x^{3} + 9 x^{2}\) - \(-1 x^{2} + 9 x + 3\) If you have any further queries or want more details, feel free to ask!