Q.Convert $Y = (A + B)(A + C)$ into canonical POS form

A canonical (standard) POS form must have every sum (OR) term containing all three variables. Each OR term is expanded by ORing it with the AND of any missing variable and its complem …

[!TLDR]

Fill in the missing variable in each OR term of $Y = (A + B)(A + C)$ so every sum term holds all of A, B and C, giving the three-maxterm canonical POS.

In a canonical (standard) POS expression each OR term must contain every input variable. We use the identity $X\overline{X} = 0$: a sum term is ORed with $X\overline{X}$ for each missing variable X and then distributed using $P + QR = (P + Q)(P + R)$.

Term $(A + B)$: variable C is missing, so OR with $C\overline{C}$:

Term $(A + C)$: variable B is missing, so OR with $B\overline{B}$: …