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The compound (a) methyl 3-oxo-3-phenylpropanoate is formed by a cross condensation reaction between the two carbonyl compounds: dimethyl carbonate and methyl phenyl ketone.

Out of these two carbonyl compounds,methyl phenyl carbonate only has the alpha-hydrogen, so it is added slowly to the basic solution of the dimethyl carbonate(does not have alpha-hydrogen).

The formation of methyl 3-oxo-3-phenylpropanoate is shown as follows:

Formation of methyl 3-oxo-3-phenylpropanoate (a)

The compound (b) 1-phenylbutane-1,3-dione is formed by a cross condensation reaction between the two carbonyl compounds: methyl acetate and methyl phenyl ketone.

Both carbonyl compounds have the alpha-hydrogen, so Lithium diisopropylamide (LDA strong base) is used to form the base from the methyl phenyl ketone and methyl acetate slowly.

The formation of 1-phenylbutane-1,3-dione is shown as follows:

Formation of 1-phenylbutane-1,3-dione (b)

The compound (c) methyl 3-oxo-3-phenylpropanal is formed by a cross condensation reaction between the two carbonyl compounds: methyl formate and methyl phenyl ketone.

Out of these two carbonyl compounds,methyl phenyl ketone only has the alpha-hydrogen, so it is added slowly to the basic solution of the methyl formate(does not have alpha-hydrogen).

The formation of methyl 3-oxo-3-phenyl propanol is shown as follows:

Formation of methyl 3-oxo-3-phenylpropanal (c)