[tex]\boxed{(5\sqrt{2}-4\sqrt{3})(5\sqrt{2}-4\sqrt{3})=98-40\sqrt{6}}[/tex]
Here we have the following expression:
[tex](5\sqrt{2}-4\sqrt{3})(5\sqrt{2}-4\sqrt{3})[/tex]
We know that:
[tex](a-b)(a-b)=(a-b)^2=a^2-2ab+b^2[/tex]
So:
[tex]a=5\sqrt{2} \\ \\ b=4\sqrt{3} \\ \\ \\ (5\sqrt{2}-4\sqrt{3})(5\sqrt{2}-4\sqrt{3})=(5\sqrt{2})^2-2(5\sqrt{2})(4\sqrt{3})+(4\sqrt{3})^2 \\ \\ (5\sqrt{2}-4\sqrt{3})(5\sqrt{2}-4\sqrt{3})=25(2)-40\sqrt{2\times 3}+16(3) \\ \\ (5\sqrt{2}-4\sqrt{3})(5\sqrt{2}-4\sqrt{3})=50-40\sqrt{6}+48 \\ \\ \\ Finally: \\ \\ \boxed{(5\sqrt{2}-4\sqrt{3})(5\sqrt{2}-4\sqrt{3})=98-40\sqrt{6}}[/tex]
Distributive Property: https://brainly.com/question/10794694
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