\[\boxed{\text{424\ (424).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
Пояснение.
Решение.
\[\textbf{а)}\ \left( 2\sqrt{5} + 1 \right)\left( 2\sqrt{5} - 1 \right) =\]
\[= \left( 2\sqrt{5} \right)^{2} - 1 = 4 \cdot 5 - 1 =\]
\[= 20 - 1 = 19\]
\[\textbf{б)}\ \left( 5\sqrt{7} - \sqrt{13} \right)\left( 5\sqrt{7} + \sqrt{13} \right) =\]
\[= \left( 5\sqrt{7} \right)^{2} - \left( \sqrt{13} \right)^{2} =\]
\[= 25 \cdot 7 - 13 =\]
\[= 175 - 13 = 162\]
\[\textbf{в)}\ \left( 3\sqrt{2} - 2\sqrt{3} \right)\left( 2\sqrt{3} + 3\sqrt{2} \right) =\]
\[= \left( 3\sqrt{2} \right)^{2} - \left( 2\sqrt{3} \right)^{2} =\]
\[= 9 \cdot 2 - 4 \cdot 3 =\]
\[= 18 - 12 = 6\]
\[\textbf{г)}\ \left( 1 + 3\sqrt{5} \right)^{2} =\]
\[= 1 + 2 \cdot 1 \cdot 3\sqrt{5} + \left( 3\sqrt{5} \right)^{2} =\]
\[= 1 + 6\sqrt{5} + 9 \cdot 5 = 46 + 6\sqrt{5}\]
\[\textbf{д)}\ \left( 2\sqrt{3} - 7 \right)^{2} =\]
\[= \left( 2\sqrt{3} \right)^{2} - 2 \cdot 2\sqrt{3} \cdot 7 + 7^{2} =\]
\[= 4 \cdot 3 - 28\sqrt{3} + 49 =\]
\[= 61 - 28\sqrt{3}\]
\[\textbf{е)}\ \left( 2\sqrt{10} - \sqrt{2} \right)^{2} =\]
\[= \left( 2\sqrt{10} \right)^{2} - 2 \cdot 2\sqrt{10} \cdot \sqrt{2} + \left( \sqrt{2} \right)^{2} =\]
\[= 4 \cdot 10 - 4\sqrt{20} + 2 = \ 42 - 8\sqrt{5}\]