Answer
$(3x+y)^{3}=27x^{3}+27x^{2}y+9xy^{2}+y^{3}$
Work Step by Step
$(3x+y)^{3}$
Rewrite this expression as $(3x+y)(3x+y)(3x+y)$:
$(3x+y)^{3}=(3x+y)(3x+y)(3x+y)=...$
First, evaluate $(3x+y)(3x+y)$ and simplify:
$...=(9x^{2}+3xy+3xy+y^{2})(3x+y)=...$
$...=(9x^{2}+6xy+y^{2})(3x+y)=...$
Finally, evaluate $(9x^{2}+6xy+y^{2})(3x+y)$ and simplify again:
$...=27x^{3}+9x^{2}y+18x^{2}y+6xy^{2}+3xy^{2}+y^{3}=...$
$...=27x^{3}+27x^{2}y+9xy^{2}+y^{3}$
