Q.Convert $(A + C)(B + \overline{C})$ into canonical POS.

In a canonical POS each sum term must contain all three variables. Every incomplete sum term is expanded by adding $(X\overline{X}) = 0$, i.e. by $(\text{term} + X\overline{X})$ factored into two complete sum terms, then the distinct maxterms are collected. …

[!TLDR]

Expanding each sum term to all three variables gives $(A+C)(B+\overline{C}) = \prod M(0,1,2,5)$.

A canonical (standard) POS expression is a product of maxterms — every sum term contains all the variables. The given expression $Y = (A + C)(B + \overline{C})$ has sum terms missing one variable each, so each is expanded using the identity $X + YZ = (X+Y)(X+Z)$, adding the missing variable as $(\text{variable})(\overline{\text{variable}})$.

Expand $(A + C)$ (missing B):

$A + C = A + C + B\overline{B} = (A + B + C)(A + \overline{B} + C)$ → maxterms $M_0, M_2$.

Expand $(B + \overline{C})$ (missing A): …