## Calculus with Applications (10th Edition)

$(3x+y)^{3}=27x^{3}+27x^{2}y+9xy^{2}+y^{3}$
$(3x+y)^{3}$ 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: $...=27x^{3}+9x^{2}y+18x^{2}y+6xy^{2}+3xy^{2}+y^{3}=...$ $...=27x^{3}+27x^{2}y+9xy^{2}+y^{3}$