Answer
$x^2+y^2+2xy+2x+2x+1$
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: $[(x+y)+1)]^2=(x+y)^2+2(x+y)+1^2=x^2+y^2+2\cdot x\cdot y+2x+2x+1^2=x^2+y^2+2xy+2x+2x+1$