1. 3(5√2) =
2. (2√3)(√15) =
3. 3(2√3-4√5) =
4. √3(5√6+4√3) =
5. (1+√2)(3+√2) =
6. (√2+√12)(√18+3√3) =
7. (√3-2√5)(√3-2√5) =
8. (3-√5)(3+√5) =
9. (2√3+√2)(2√3-√2)=
10. (1³√8)(4+³√2)=

Let's solve these step by step:

1. **\( 3(5\sqrt{2}) \)**
   \[
   3 \times 5\sqrt{2} = 15\sqrt{2}
   \]

2. **\( (2\sqrt{3})(\sqrt{15}) \)**
   \[
   2\sqrt{3} \times \sqrt{15} = 2\sqrt{3 \times 15} = 2\sqrt{45} = 2 \times 3\sqrt{5} = 6\sqrt{5}
   \]

3. **\( 3(2\sqrt{3} - 4\sqrt{5}) \)**
   \[
   3 \times 2\sqrt{3} - 3 \times 4\sqrt{5} = 6\sqrt{3} - 12\sqrt{5}
   \]

4. **\( \sqrt{3}(5\sqrt{6} + 4\sqrt{3}) \)**
   \[
   \sqrt{3} \times 5\sqrt{6} + \sqrt{3} \times 4\sqrt{3} = 5\sqrt{18} + 4\sqrt{9} = 5 \times 3\sqrt{2} + 4 \times 3 = 15\sqrt{2} + 12
   \]

5. **\( (1 + \sqrt{2})(3 + \sqrt{2}) \)**
   \[
   1 \times 3 + 1 \times \sqrt{2} + \sqrt{2} \times

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