Multiply the binomial and find the coefficients

(X+y) ^1=__*+__y

(*+y) ^2=__x^2+__xy+__y^2

(X+y) ^3=__*^3+__*^2y+__y^3

(*+y) ^4=__*^4+__x^3y+__x^2y^2+__xy^3+__y4

We can use the pascal triangle to solve this problem.

For this case, rewriting each binomial we have:

(x + y) ^ 1 = 1x + 1y

(x + y) ^ 2 = 1x ^ 2 + 2xy + 1y ^ 2

(x + y) ^ 3 = 1x ^ 3 + 3x ^ 2y + 3xy ^ 2 + 1y ^ 3

(x + y) ^ 4 = 1x ^ 4 + 4x ^ 3y + 6x ^ 2y ^ 2 + 4xy ^ 3 + 1y4