18 Simplify the following (a) (5-47)(7+35) (b) (11-4)(2+3) (c) (65-23)(35-25) (d) (112+2)(2+32)

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\frac{32}{5} + \frac{23}{11} \times \frac{22}{15}

\frac{32}{5} + \frac{23}{11} \times \frac{22}{15}

Simplify the following:
$12 + 22 \div 11 \times (18 \div 3)^{2} - 10$

1^{2} = \frac{1}{6} [1 \times (1 + 1) \times (2 \times 1 + 1)] 1^{2} + 2^{2} = \frac{1}{6} [2 \times (2 + 1) \times (2 \times 2 + 1)] 1^{2} + 2^{2} + 3^{2} = \frac{1}{6} [3 \times (3 + 1) \times (2 \times 3 + 1)] 1^{2} + 2^{2} + 3^{2} + 4^{2} = \frac{1}{6} [4 \times (4 + 1) \times (2 \times 4 + 1)]

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

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

(6 - \sqrt{6}) (6 + \sqrt{6})

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

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

{(3 - \sqrt{3})}^{2}

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