what is the following product?\n$(x\\sqrt{7}-3\\sqrt{8})(x\\sqrt{7}-3\\sqrt{8})$ \n$7x^{2}+72$\n$7x^{2}-12x\\…

Explanation:

Step1: Recognize the form

The expression ((x\sqrt{7}-3\sqrt{8})(x\sqrt{7}-3\sqrt{8})) is in the form ((a - b)^2) where (a=x\sqrt{7}) and (b = 3\sqrt{8}). Using the formula ((a - b)^2=a^{2}-2ab + b^{2}).

Step2: Calculate (a^{2})

(a^{2}=(x\sqrt{7})^{2}=x^{2}\times(\sqrt{7})^{2}=7x^{2})

Step3: Calculate (2ab)

First, simplify (\sqrt{8}=2\sqrt{2}). Then (2ab = 2\times(x\sqrt{7})\times(3\sqrt{8})=2\times x\sqrt{7}\times3\times2\sqrt{2}=12x\sqrt{14})

Step4: Calculate (b^{2})

(b^{2}=(3\sqrt{8})^{2}=3^{2}\times(\sqrt{8})^{2}=9\times8 = 72)

Step5: Combine the terms

((x\sqrt{7}-3\sqrt{8})^{2}=7x^{2}-12x\sqrt{14}+72)

Answer:

(7x^{2}-12x\sqrt{14}+72)