The discussion focuses on the partial fraction decomposition of the expression 4x²y divided by the product of two quadratic polynomials. A clever algebraic manipulation is suggested to simplify the expression, leading to the identification of 4xy as the difference of two quadratic terms. The proposed decomposition involves expressing the original fraction as a sum of two simpler fractions, each with one of the quadratic polynomials in the denominator. Through coefficient comparison, the values for A and D are determined, resulting in the final decomposition of the expression. The solution demonstrates an effective approach to tackling complex algebraic fractions.