How could each of the following compounds be prepared from cyclohexanone?

a.

b.

c.

The process of alkylation of the $\alpha$-carbon is done by removing protons present on the$\alpha$-carbon using a strong base (LDA) and THF solvent. A strong base forms an enolate ion, and then the addition of alkyl halide to the enolate ion takes place.

Formation of alkylated $\mathrm{\alpha }$-carbon compound

Formation of alkylated $\mathrm{\alpha }$-carbon compound

(c) The given compound is prepared when benzyl bromide is treated with cyclohexanone (symmetrical ketone). A strong base LDA and THF solvent are added to cyclohexanone, making an enolate ion. After this, benzyl bromide is added to enolate ion, where the alkyl group of benzyl bromide is added to the $\alpha$-carbon of the cyclohexanone compound.

Formation of alkylated $\alpha$-carbon compound