11. \( -2 m^{2} x-m^{2}-m^{2} x^{2} \)

To tackle the expression \( -2 m^{2} x - m^{2} - m^{2} x^{2} \), we can first rearrange and combine like terms to get a clearer picture. Collecting the terms helps us look for common factors. The expression can be rewritten as \( -m^2 x^2 - 2m^2 x - m^2 \). Here, you can factor out \(-m^2\), leading to \( -m^2(x^2 + 2x + 1) \). This neatens things up and allows us to see the quadratic inside the parentheses, which can be factored again to \(-m^2(x + 1)^2\). Understanding how to simplify algebraic expressions not only makes math easier but also lays the groundwork for solving more complex equations. It's like decluttering a messy room – once everything's in order, you can find what you need quickly! When facing similar algebraic expressions, a common mistake is forgetting to combine like terms or misplacing negative signs, which can lead to wrong answers. Double-check your steps, and if you're ever unsure, break the expression down into smaller parts. This problem-solving strategy is vital; it keeps errors to a minimum and helps you build confidence in your math abilities!