$a)_{}$ $(a+b+1)^3-(a+b-1)-6.(a+b)^2_{}$
$=a^3+b^3+1+3a^2b+3ab^2+3b^2+3a+3b+6ab-(a^3+b^3-1+3a^2b-3a^2+3ab^2-3b^2+3a+3b-6ab)-6.(a^2+2ab+b^2)_{}$
$=a^3+b^3+1+3a^2b+3a^2+3ab^2+3b^2+3a+3b+6ab-a^3-b^3+1-3a^2b+3a^2-3ab^2+3b^2-3a-3b+6ab-6a^2-12ab-6b^2_{}$
$=2_{}$