a2 - 4ab + 5b2 - 4bc + 4c2
= a2 - 4ab + 4b2 + 4c2 - 4bc + b2
= (a - 2b)2 + (2c - b)2
\(a^2-4ab+5b^2-4bc+4c^2\)
\(=a^2-4ab+4b^2+b^2-4bc+4c^2\)
\(=a^2-2.a.2b+\left(2b\right)^2+b^2-2.b.2c+\left(2c\right)^2\)
\(=\left(a-2b\right)^2+\left(b-2c\right)^2\)