<s>[INST] Evaluate $(\sqrt{5}+\sqrt{6}+\sqrt{7})(\sqrt{5}+\sqrt{6}-\sqrt{7})(\sqrt{5}-\sqrt{6}+\sqrt{7})(-\sqrt{5}+\sqrt{6}+\sqrt{7})$ Evaluate $(\sqrt{5}+\sqrt{6}+\sqrt{7})(\sqrt{5}+\sqrt{6}-\sqrt{7})(\sqrt{5}-\sqrt{6}+\sqrt{7})(-\sqrt{5}+\sqrt{6}+\sqrt{7})$
I find out the answer $104$ but my friend find the answer $96$ using calculator.which one is correct?
 [/INST] Hint:
let $x=\sqrt(5)+\sqrt(6)$ and $y=\sqrt(5)-\sqrt(6)$
so 
$$(x+\sqrt{7})(x-\sqrt{7})(y+\sqrt{7})(-y+\sqrt{7})$$
then you can use the fact of
$$(a-b)(a+b)=a^2-b^2$$
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