We look at two examples of homotopy Lie algebras (also known as L_{\infty}
algebras) in detail from two points of view. We will exhibit the algebraic
point of view in which the generalized Jacobi expressions are verified by using
degree arguments and combinatorics. A second approach using the nilpotency of
Grassmann-odd differential operators \Delta to verify the homotopy Lie data is
shown to produce the same results.