Answer
$81x^4+108x^3+54x^2+12x+1$
Work Step by Step
We are given the expression:
$(3x+1)^4$
Use the Binomial Theorem to expand the expression:
$(3x+1)^4=\sum_{k=0}^4 \binom{4}{k}(3x)^{4-k}(1)^k$
$=\binom{4}{0}(3x)^4(1)^0+\binom{4}{1}(3x)^3(1)^1+\binom{4}{2}(3x)^2(1)^2+\binom{4}{3}(3x)^1(1)^3+\binom{4}{4}(3x)^0(1)^4$
$=81x^4+4(27)x^3+6(9)x^2+4(3)x^1+1$
$=81x^4+108x^3+54x^2+12x+1$
