Answer
$27x^3+27x^2y+9xy^2+y^3$
Work Step by Step
Binomial Theorem or Binomial expansion can be defined as:
$(x+y)^n=\displaystyle \binom{n}{0}x^ny^0+\displaystyle \binom{n}{1}x^{n-1}y^1+........+\displaystyle \binom{n}{n}x^0y^n$
Need to apply the formula to get the Binomial Expansion.
we have
$(3x+y)^3=\displaystyle \binom{3}{0}(3x)^3y^0+\displaystyle \binom{3}{1}(3x^{2})y^1
+\displaystyle \binom{3}{2}(3x)^1y^2+\displaystyle \binom{3}{3}(3x)^0y^3$
$=27x^3(1)+3(9x^2)y+9xy^2+y^3(1)$ $\bf{(Simplify)}$
$=27x^3+27x^2y+9xy^2+y^3$
