Question

Simplify

Answer 1

\[(\sqrt{5} + \sqrt{6} + \sqrt{7}) (-\sqrt{5} + \sqrt{6} + \sqrt{7}) (\sqrt{5} - \sqrt{6} + \sqrt{7}) (\sqrt{5} + \sqrt{6} + \sqrt{7})\]

Answer 2

@ParthKohli @lgbasallote @FoolForMath @dpaInc @.Sam. @Mertsj @jim_thompson5910 @Mertsj @myininaya @Limitless

Answer 3

can't we use our regular a^2 - b^2 ??

Answer 4

yes but it to look simple I done that

Answer 5

You can arrange it like this too
\[\left(\sqrt{5}+\sqrt{6}+\sqrt{7}\right)^2\left(\sqrt{5}-\sqrt{6}+\sqrt{7}\right) \left(-\sqrt{5}+\sqrt{6}+\sqrt{7}\right) \]

Answer 6

^that's the only intelligent observation to be made in this problem, I believe.

Answer 7

wait one is (sqrt5+sqrt6-sqrt7)

Answer 8

\[(\sqrt{5} + \sqrt{6} + \sqrt{7}) (-\sqrt{5} + \sqrt{6} + \sqrt{7}) (\sqrt{5} - \sqrt{6} + \sqrt{7}) (\sqrt{5} + \sqrt{6} - \sqrt{7})\]

Answer 9

right

Answer 10

If you expand, 5 cancels 5 , 6 cancels 6 , cancels 7

Answer 11

I tried to much even changing them to a=sqrt5 b=sqrt6 c=sqrt7

Answer 12

\[[(a+b+c)(a-b+c)] [(-a+b+c)(a+b-c)]\]
\[[a^2+2ac-b^2+c^2] [-a^2+2ac+b^2-c^2]\]
\[[5+2\sqrt{5}\sqrt{6}-6+7][-5+2\sqrt{5}\sqrt{6}+6-7]\]
\[[5+2\sqrt{5}\sqrt{6}-6+7][-5+2\sqrt{5}\sqrt{6}+6-7]\]
\[[6+2\sqrt{5}\sqrt{6}][-6+2\sqrt{5}\sqrt{6}]\]