Question

Find the value of
$( \sqrt{3} + 1) ^{4} - ( \sqrt{3} - 1) ^{4}$
​

Answer 1

Answer:

$(\sqrt{3} +1)^4$ - $(\sqrt{3} -1)^4$=32$\sqrt{3}$

Step-by-step explanation:

$(\sqrt{3} +1)^4$

=9+1+$\sqrt{3}$(12+6$\sqrt{3}$+4)

=10+12$\sqrt{3}$+18+4$\sqrt{3}$=28+16$\sqrt{3}$

$(\sqrt{3} -1)^4$

=9+1-$\sqrt{3}$(12-6$\sqrt{3}$+4)

=10-12$\sqrt{3}$+18-4$\sqrt{3}$=28-16$\sqrt{3}$

$(\sqrt{3} +1)^4$ - $(\sqrt{3} -1)^4$

=28+16$\sqrt{3}$-28+16$\sqrt{3}$=32$\sqrt{3}$