The author considers the problem of writing the product of two polynomials as the sum of other polynomials. The polynomials are given as the sum of orthogonal polynomials, and he uses the comrade matrix to encode some of the calculations. The calculations are done directly using the three term recurrence relation rather than using powers of x as an intermediate step. A few specific examples are stated at the end, including Legrende and Hermite polynomials. The author claims his method is more systematic than that of guessing the coefficients in the linearization and proving them by induction. The reviewer does not understand this, for he does not understand how the coefficient can be found explicitly in the examples given without doing some calculations, seeing a pattern, and proving it by induction.