one carbon elongation

1. aldehyde to aldehyde
step 1. aldehyde + PPh3Cl-CH2OMe/t-BuOK
step 2. Formic acid.

Wiki is a good source of infomation:

Examples of homologation reactions include:

• Seyferth-Gilbert homologation
• Displacement of a halide by a cyanide group, which can be reduced to an amine, see: Kolbe nitrile synthesis
• Kiliani-Fischer synthesis, where an aldose molecule is elongated through a three-step process consisting of:
  1. Nucleophillic addition of cyanide to the carbonyl to form a cyanohydrin
  2. Hydrolysis to form a lactone
  3. Reduction to form the homologous aldose
• Wittig reaction of an aldehyde with methoxymethylenetriphenylphosphine, which produces a homologous aldehyde.
• Arndt-Eistert synthesis is a series of chemical reactions designed to convert a carboxylic acid to a higher carboxylic acid homologue (ie. contains one additional carbon atom)
• Kowalski ester homologation, an alternative to the Arndt-Eistert synthesis. Has been used to convert β-amino esters from α-amino esters through an ynolate intermediate.^[2]

Some reactions increase the chain length by more than one unit. For example, the following are considered two-carbon homologation reactions:

• Nucleophilic addition to ethylene oxide, resulting in a ring-opening and producing a primary alcohol with two extra carbons.
• Malonic ester synthesis, which produces a carboxylic acid with two extra carbons.