a) \(=a^2+2ab+1-\left(a^2-2ab+1\right)-3\left(a^2-1\right)\)
\(=a^2+2ab+1-a^2+2ab-1-3a^2+1\)
\(=4ab-3a^2+1\)
b) \(=\left(m^6+m+1-2m^4-2m+2m^3\right)+\left(m^4-9m^2+9\right)-2\left(m^2-3\right)\left(m^2-m+1\right)\)
\(=m^6+m+1-2m^4-2m+2m^3+m^4-9m^2+9-2\left(m^2-3\right)\left(m^2-m+1\right)\)\(=m^6-m+10-m^4+2m^3-9m^2-\left(2m^4-m^3+m^2-3m^2+3m-3\right)\)
\(=m^6-m+10-m^4+2m^3-9m^2-2m^4-m^3+m^2-3m^2+3m-3\)
\(=m^6+m^3-11m^2-3m^4+2m+7\)
a: \(=a^2+2a+1-a^2+2a-1-3a^2+3=-3a^2+4a+3\)
b: \(=\left(m^2-m+1-m^2+3\right)^2=\left(4-m\right)^2\)
\(=16-8m+m^2\)