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  4. (√3+1)4+(√3-1)4 is a/an

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Q. $\left(\sqrt{3}+1\right)^{4}+\left(\sqrt{3}-1\right)^{4}$ is a/an

Binomial Theorem

Solution:

We have, $\left(\sqrt{3}+1\right)^{4}+\left(\sqrt{3}-1\right)^{4}$
$= 2\left(\,{}^{4}C_{0}\left(\sqrt{3}\right)^{4}+\,{}^{4}C_{2}\left(\sqrt{3}\right)^{2}+\,{}^{4}C_{4}\left(\sqrt{3}\right)^{0}\right)$
$= 2\left(9 + 18 + 1\right) = 56$.