Let's simplify the expression $1 + 3\sqrt{2} - (4 - \sqrt{50})$.

Step-by-step solution:

1. Distribute the negative sign across the parentheses: $1 + 3\sqrt{2} - 4 + \sqrt{50}$

2. Simplify the constants: $1 - 4 = -3$ So the expression becomes: $-3 + 3\sqrt{2} + \sqrt{50}$

3. Simplify $\sqrt{50}$: $\sqrt{50} = \sqrt{25 \times 2} = 5\sqrt{2}$ Now the expression is: $-3 + 3\sqrt{2} + 5\sqrt{2}$

4. Combine the like terms $3\sqrt{2} + 5\sqrt{2}$: $3\sqrt{2} + 5\sqrt{2} = 8\sqrt{2}$ So the final simplified expression is: $-3 + 8\sqrt{2}$

Thus, the simplified expression is: $-3 + 8\sqrt{2}$

Would you like more details on any part of this process? Here are some related questions:

1. What is the general method to simplify expressions with square roots?
2. How do you factor square roots like $\sqrt{50}$ into simpler terms?
3. What are like terms, and how do you combine them?
4. How do you handle parentheses in algebraic expressions?
5. What is the importance of distributive property in simplifying expressions?

Tip: Always check if square roots can be simplified by factoring out perfect squares.