Answer
We can find the coefficients in the expansion of $(a+b)^{n}$ from the nth row of Pascal's triangle.
So $(a+b)^{4}$ = $a^{4} + 4a^{3}b + 6a^{2}b^{2} + 4ab^{3} + b^{4}$
Work Step by Step
To find the coefficients of the expansion of a binomial look at the rows of Pascal's triangle. When n =4 look at the fourth row - the coefficients (from the fourth row of Pascal's Triangle) are 1 4 6 4 1 - plug these into the binomial expansion.