$$( 5 \sqrt { 3 } - 2 \sqrt { 2 } ) ( 5 \sqrt { 3 } + 2 \sqrt { 2 } )$$
$67$
$$\left(5\sqrt{3}\right)^{2}-\left(2\sqrt{2}\right)^{2}$$
$$5^{2}\left(\sqrt{3}\right)^{2}-\left(2\sqrt{2}\right)^{2}$$
$$25\left(\sqrt{3}\right)^{2}-\left(2\sqrt{2}\right)^{2}$$
$$25\times 3-\left(2\sqrt{2}\right)^{2}$$
$$75-\left(2\sqrt{2}\right)^{2}$$
$$75-2^{2}\left(\sqrt{2}\right)^{2}$$
$$75-4\left(\sqrt{2}\right)^{2}$$
$$75-4\times 2$$
$$75-8$$
$$67$$
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