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

what is the following product?\n$(x\\sqrt{7}-3\\sqrt{8})(x\\sqrt{7}-3\\sqrt{8})$ \n$7x^{2}+72$ \n$7x^{2}-12x\\sqrt{14}+72$ \n$7x^{2}-12x\\sqrt{14}-72$ \n$7x^{2}-72$

what is the following product?\n$(x\\sqrt{7}-3\\sqrt{8})(x\\sqrt{7}-3\\sqrt{8})$ \n$7x^{2}+72$ \n$7x^{2}-12x\\sqrt{14}+72$ \n$7x^{2}-12x\\sqrt{14}-72$ \n$7x^{2}-72$

Answer

Explanation:

Step1: Use FOIL method

((a - b)(a - b)=a^{2}-2ab + b^{2}), where (a = x\sqrt{7}) and (b=3\sqrt{8}). First terms: ((x\sqrt{7})\times(x\sqrt{7})=x^{2}\times\sqrt{7}\times\sqrt{7}=7x^{2}) Outer terms: ((x\sqrt{7})\times(- 3\sqrt{8})=-3x\sqrt{56}=-3x\sqrt{4\times14}=-6x\sqrt{14}) Inner terms: ((-3\sqrt{8})\times(x\sqrt{7})=-3x\sqrt{56}=-6x\sqrt{14}) Last terms: ((-3\sqrt{8})\times(-3\sqrt{8})=9\times\sqrt{8}\times\sqrt{8}=9\times8 = 72)

Step2: Combine like - terms

(7x^{2}-6x\sqrt{14}-6x\sqrt{14}+72=7x^{2}-12x\sqrt{14}+72)

Answer:

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