Answer
$x^{6}$ + 6$x^{5}$$y^{1}$ + 15$x^{4}$$y^{2}$ + 20$x^{3}$$y^{3}$ + 15$x^{2}$$y^{4}$ + 6$x^{1}$$y^{5}$ + $y^{6}$
Work Step by Step
We know by Binomial theorem
$(x+y)^{n}$ = C(n,0)$x^{n}$ + C(n,1)$x^{n-1}$$y^{1}$ .... + C(n,n)$y^{n}$
By applying the above result to $(x+y)^{6}$ we get
$(x+y)^{6}$ = C(6,0)$x^{6}$ + C(6,1)$x^{5}$$y^{1}$ + C(6,2)$x^{4}$$y^{2}$ + C(6,3)$x^{3}$$y^{3}$ + C(6,4)$x^{2}$$y^{4}$ + C(6,5)$x^{1}$$y^{5}$ + C(6,6)$y^{6}$
= $x^{6}$ + 6$x^{5}$$y^{1}$ + 15$x^{4}$$y^{2}$ + 20$x^{3}$$y^{3}$ + 15$x^{2}$$y^{4}$ + 6$x^{1}$$y^{5}$ + $y^{6}$
