Answer
$81x^4+108x^3+54x^2+12x+1$
Work Step by Step
According to the Binomial Theorem or Binomial expansion, the expansion for $(x+y)$ in the any number of power can be calculated as:
$(x+y)^n=\displaystyle \binom{n}{0}x^ny^0+\displaystyle \binom{n}{1}x^{n-1}y^1+........+\displaystyle \binom{n}{n}x^0y^n$
Let's see how this formula works:
$(3x+1)^4=\displaystyle \binom{4}{0}(3x)^4(1)^0+\displaystyle \binom{4}{1}(3x)^3(1)^1+\displaystyle \binom{4}{2}(3x)^2(1)^2+\displaystyle \binom{4}{3}(3x)^1(1)^3+\displaystyle \binom{4}{4}(3x)^0(1)^3$
or, $=81x^4+4(27x^3)(1)+6(9x^2)+12x+1$
or, $=81x^4+108x^3+54x^2+12x+1$
