Answer
$(x+3y)(x^2-3xy+9y^2)$.
Work Step by Step
An expression is factored completely if it is written as a product of factors so that none of its factors can be further factored.
Rewrite the given expression as a sum of cubes.
$x^3+27y^3=x^3+(3y)^3$
Use the algebraic identity.
$a^3+b^3=(a+b)(a^2-ab+b^2)$
where $a=x$ and $b=3y$.
$=(x+3y)[(x)^2-(x)(3y)+(3y)^2]$
Simplify.
$=(x+3y)(x^2-3xy+9y^2)$.
