What is the coefficient of x in expansion of (x+3)^5 ?

Consider the binomial expansion of (1 + x)ⁿ, which is the binomial theorem.



Thus, we can say that the expansion of (3 + x)⁵ is:



We can see that the only way to have an x-value in the expansion is when r = 1. Substituting r = 1 into the expansion, we get:






Thus, the coefficient of the x term is 405, based on our binomial theorem.