Expand and Simplify into the Form $a + b \sqrt{c}$

1)

(3 + \sqrt{2}) (4 + \sqrt{2})

14 + 7 \sqrt{2}

2)

(5 + \sqrt{3}) (2 - \sqrt{3})

7 - 3 \sqrt{3}

3)

(2 + \sqrt{18}) (3 + \sqrt{2})

12 + 11 \sqrt{2}

4)

(3 - \sqrt{5}) (4 + \sqrt{45})

- 3 + 5 \sqrt{5}

5)

(5 - \sqrt{3}) (2 - \sqrt{27})

19 - 17 \sqrt{3}

6)

(\sqrt{18} - \sqrt{8}) (\sqrt{2} - \sqrt{1})

2 - \sqrt{2}

7)

{(6 + \sqrt{3})}^{2} - {(5 - \sqrt{3})}^{2}

11 + 22 \sqrt{3}

8)

{(2 \sqrt{5} - 4)}^{2} - {(3 + 3 \sqrt{5})}^{2}

- 18 - 34 \sqrt{5}