\(=a^4-a^3+a^3-a^2+2a^2-2a+2a-2\\ =\left(a-1\right)\left(a^3+a^2+2a+2\right)\\ =\left(a-1\right)\left(a+1\right)\left(a^2+2\right)\)
\(=a^4+2a^2-a^2-2\)
\(=\left(a^2+2\right)\left(a^2-1\right)\)
\(=\left(a^2+2\right)\left(a-1\right)\left(a+1\right)\)