Substation method fails to prove that $T(n) = \Theta(n^2) $ for the recursion $T(n)= 4T(n/2) + n^2$, since you end up with $T(n) < cn^2 \leq cn^2 + n^2 $.
I don't understand how to subtract off lower-order term to prove that substation works.
Came up with: $T(n) \leq cn^2 - bn^2$ Assume it holds for $T(n/2) \leq c(n/2)^2 - b(n/2)^2$
$T(n) \leq 4(c(n/2)^2 - b(n/2)^2) + n^2 = cn^2- bn^2 + n^2 $
However, you there is no way to solve $cn^2- bn^2 + n^2 \leq cn^2 - bn^2 $ for $b$
But I am not sure if I am going in the right direction, though mathematics is very elementary. Thanks !