Benzoin condensation: 2 ArCHO + NaCN (catalyst) → ArCH(OH)COAr (alpha-hydroxy ketone / benzoin)

• NaCN acts as a catalyst (not consumed) — cyanide ion is a nucleophilic catalyst (umpolung)
• The cyanide makes the carbonyl carbon nucleophilic (polarity reversal)

Perkin reaction: ArCHO + (RCO)2O + RCOONa → ArCH=C(R)COOH (alpha,beta-unsaturated acid)

• Classic: PhCHO + (CH3CO)2O + CH3COONa → PhCH=CHCOOH (cinnamic acid)
• Acetic anhydride provides the alpha-H; its enolate attacks the aldehyde C=O

Knoevenagel condensation: ArCHO + active methylene compound (malonic acid, etc.) + weak base → alpha,beta-unsaturated product with loss of CO2