Answer
$(x+y+3)^2$
Work Step by Step
The product of a binomial sum and a binomial difference is: $(A+B)(A-B)=A^2-B^2$.
The square of a binomial sum is: $(A+B)^2=A^2+2AB+B^2$.
The square of a binomial difference is: $(A-B)^2=A^2-2AB+B^2$.
Hence here: $(x+y)^2+6(x+y)+9=\\=(x+y)^2+2\cdot(x+y)\cdot3+3^2\\=(x+y+3)^2$
