what is the following product?\n$(5\\sqrt{2}-4\\sqrt{3})(5\\sqrt{2}-4\\sqrt{3})$ \n-2\n2\n$22…

Explanation:

Step1: Recognize the form

The expression ((5\sqrt{2}-4\sqrt{3})(5\sqrt{2}-4\sqrt{3})) is in the form ((a - b)^2) where (a = 5\sqrt{2}) and (b=4\sqrt{3}). The formula ((a - b)^2=a^{2}-2ab + b^{2}).

Step2: Calculate (a^{2})

(a^{2}=(5\sqrt{2})^{2}=5^{2}\times(\sqrt{2})^{2}=25\times2 = 50).

Step3: Calculate (2ab)

(2ab=2\times(5\sqrt{2})\times(4\sqrt{3})=2\times5\times4\times\sqrt{2\times3}=40\sqrt{6}).

Step4: Calculate (b^{2})

(b^{2}=(4\sqrt{3})^{2}=4^{2}\times(\sqrt{3})^{2}=16\times3 = 48).

Step5: Find the result

((5\sqrt{2}-4\sqrt{3})^{2}=a^{2}-2ab + b^{2}=50-40\sqrt{6}+48=98 - 40\sqrt{6}).

Answer:

(98 - 40\sqrt{6})