\(=a^2-\left(b^2+4c^2-4bc\right)-b^2+bc+2c^2-ab-ac\)
\(=a^2-\left(b-2c\right)^2-\left(b+c\right)\left(b-2c\right)-a\left(b+c\right)\)
\(=\left(a-b+2c\right)\left(a+b-2c\right)-\left(b+c\right)\left(a+b-2c\right)\)
\(=\left(a+b-2c\right)\left(a-2b+c\right)\)