Multiply and simplify. $$ (\sqrt{2}+7 \sqrt{5})(\sqrt{3}+\sqrt{2}) $$

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We start with the expression:
$$
(\sqrt{2}+7\sqrt{5})(\sqrt{3}+\sqrt{2})
$$
Multiply each term in the first parenthesis by each term in the second:
$$
\sqrt{2} \cdot \sqrt{3} + \sqrt{2} \cdot \sqrt{2} + 7\sqrt{5} \cdot \sqrt{3} + 7\sqrt{5} \cdot \sqrt{2}
$$
Simplify each multiplication:
- $$\sqrt{2} \cdot \sqrt{3} = \sqrt{6}$$
- $$\sqrt{2} \cdot \sqrt{2} = 2$$
- $$7\sqrt{5} \cdot \sqrt{3} = 7\sqrt{15}$$
- $$7\sqrt{5} \cdot \sqrt{2} = 7\sqrt{10}$$

Combine these results:
$$
\sqrt{6} + 2 + 7\sqrt{15} + 7\sqrt{10}
$$

Thus, the simplified form is:
$$
2 + \sqrt{6} + 7\sqrt{10} + 7\sqrt{15}
$$
The simplified form is $$2 + \sqrt{6} + 7\sqrt{10} + 7\sqrt{15}$$.

Multiply and simplify.

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