simplify the following expression

simplify 4√32+5√12-5√50+7√75

$\begin{array}{|rcll|} \hline && 4\sqrt{32}+5\sqrt{12}-5\sqrt{50}+7\sqrt{75} \\ &=& 4\sqrt{16\cdot 2}+5\sqrt{4\cdot 3}-5\sqrt{25\cdot 2}+7\sqrt{25\cdot 3} \\ &=& 4\sqrt{16}\sqrt{2}+5\sqrt{4}\sqrt{3}-5\sqrt{25}\sqrt{2}+7\sqrt{25}\sqrt{3} \quad & | \quad \sqrt{16}= 4 \quad \sqrt{4}=2 \quad \sqrt{25} = 5 \\ &=& 4\cdot 4\cdot \sqrt{2}+5\cdot 2 \cdot \sqrt{3}-5\cdot 5 \cdot \sqrt{2}+7\cdot 5 \cdot \sqrt{3} \\ &=& 16 \sqrt{2}+10 \sqrt{3}-25\sqrt{2}+35\sqrt{3} \\ &=& 45\sqrt{3} - 9\sqrt{2} \\ \hline \end{array}$