Answer
$x^3+6\sqrt 2x^{5/2}+30x^2+40\sqrt 2x^{3/2}+60x+24\sqrt 2x^{1/2}+8$
Work Step by Step
We are given the expression:
$(\sqrt x+\sqrt 2)^6$
Use the Binomial Theorem to expand the expression:
$(\sqrt x+\sqrt 2)^6=\sum_{k=0}^6 \binom{6}{k}(\sqrt x)^{6-k}(\sqrt 2)^k$
$=\binom{6}{0}(\sqrt x)^6(\sqrt 2)^0+\binom{6}{1}(\sqrt x)^5(\sqrt 2)^1+\binom{6}{2}(\sqrt x)^4(\sqrt 2)^2+\binom{6}{3}(\sqrt x)^3(\sqrt 2)^3+\binom{6}{4}(\sqrt x)^2(\sqrt 2)^4+\binom{6}{5}(\sqrt x)^1(\sqrt 2)^5+\binom{6}{6}(\sqrt x)^0(\sqrt 2)^6$
$=x^3+6\sqrt 2x^{5/2}+15x^2(2)+20x^{3/2}(2\sqrt 2)+15x(4)+6x^{1/2}(4\sqrt 2)+8$
$=x^3+6\sqrt 2x^{5/2}+30x^2+40\sqrt 2x^{3/2}+60x+24\sqrt 2x^{1/2}+8$
