\[\left( 4\sqrt{5} - 5\sqrt{2} \right)^{2} =\]
\[= 16 \cdot 5 - 40\sqrt{5 \cdot 2} + 25 \cdot 2 =\]
\[= 80 - 40\sqrt{10} + 50 =\]
\[= 130 - 40\sqrt{10}\]