what is the product? (x square root 7 - 3 square root 8) (x square root 7 - 3 square root 8)

Answer:The product is [tex]7x^2-12x\sqrt{14}+72[/tex]Step-by-step explanation:We need to find product of:[tex](x\sqrt{7}-3\sqrt{8} )(x\sqrt{7}-3\sqrt{8})[/tex]We need to multiply these terms[tex]=x\sqrt{7}(x\sqrt{7}-3\sqrt{8})-3\sqrt{8}(x\sqrt{7}-3\sqrt{8})\\=x^2(\sqrt{7})^2-3x(\sqrt{7}*\sqrt{8})-3x(\sqrt{8}*\sqrt{7})+9(\sqrt{8})^2\\=x^2(7)-6x(\sqrt{7}*\sqrt{8})+9(8)\\=7x^2-6x\sqrt{56}+72 \\\sqrt{56}=2\sqrt{14}\\=7x^2-6x*2\sqrt{14}+72\\=7x^2-12x\sqrt{14}+72[/tex]So, the product is [tex]7x^2-12x\sqrt{14}+72[/tex]