Simplify. \( 2 \sqrt{32}-\sqrt{50}+4 \sqrt{18} \)

To simplify \( 2 \sqrt{32} - \sqrt{50} + 4 \sqrt{18} \), let's break each term down: 1. \( \sqrt{32} = \sqrt{16 \cdot 2} = 4\sqrt{2} \), so \( 2\sqrt{32} = 2 \cdot 4\sqrt{2} = 8\sqrt{2} \). 2. \( \sqrt{50} = \sqrt{25 \cdot 2} = 5\sqrt{2} \). 3. \( \sqrt{18} = \sqrt{9 \cdot 2} = 3\sqrt{2} \), so \( 4\sqrt{18} = 4 \cdot 3\sqrt{2} = 12\sqrt{2} \). Now, substituting back into the expression: \[ 2 \sqrt{32} - \sqrt{50} + 4 \sqrt{18} = 8\sqrt{2} - 5\sqrt{2} + 12\sqrt{2} \] Combine the like terms: \[ (8 - 5 + 12)\sqrt{2} = 15\sqrt{2} \] Thus, the simplified result is \[ \boxed{15\sqrt{2}} \]