(a+b+2)(a+b)-(a-b)^2+1=a^2+2ab+b^2+2a+2b-(a-b)^2+1=a^2+2ab+b^2+2a+2b-(a^2-2ab+b^2)+1=a^2+2ab+b^2+2a+2b-a^2+2ab-b^2+1=2ab+b^2+2a+2b+2ab-b^2+1=4ab+b^2+2a+2b-b^2+1=4ab+2a+2b+1=(2a+1)*(2b+1)