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

[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]

luisejr77 luisejr77 · Answer 2 · 2019-08-09T18:46:47+02:00

Answer:

[tex]7x^2-12x\sqrt{14}+72[/tex]

Step-by-step explanation:

First we write the product

(x square root 7 - 3 square root 8) (x square root 7 - 3 square root 8)

This is:

[tex](x\sqrt{7}-3\sqrt{8})(x\sqrt{7}-3\sqrt{8})[/tex]

Now apply the distributive property as shown below.

[tex](x\sqrt{7}-3\sqrt{8})(x\sqrt{7}-3\sqrt{8})=x\sqrt{7}*x\sqrt{7} -3\sqrt{8}*x\sqrt{7}-3\sqrt{8}*x\sqrt{7} +3\sqrt{8}*3\sqrt{8}[/tex]

[tex](x\sqrt{7}-3\sqrt{8})(x\sqrt{7}-3\sqrt{8})=(x\sqrt{7})^2 -6x\sqrt{7}*\sqrt{8}+9*(\sqrt{8})^2\\\\\\(x\sqrt{7}-3\sqrt{8})(x\sqrt{7}-3\sqrt{8})=7x^2 -12x\sqrt{7*2}+9*8\\\\(x\sqrt{7}-3\sqrt{8})(x\sqrt{7}-3\sqrt{8})=7x^2-12x\sqrt{14}+72[/tex]