# Coefficient of the x^2 term

28. What is the coefficient of the x^2 term in the product of (2x^2 + 3x – 4) and (3x^2 – 4x + 6)?

Only 296 out of the 729 who participated in the intermediate age group in the 3^{rd} MATH-Inic Vedic Mathematics National Challenge got the correct answer in this very easy question.

I suspect that the majority of the contestants tried to get the complete polynomial product first using the conventional multiplication method. This would require 4 lines of solution, 9 multiplication and 4 addition operations.

However, the question requires only the coefficient of the x^2 term not the complete product. You get an x^2 product if you multiply an x^2 term by a constant or by multiplying 2 x-terms.

Therefore, solving this problem is as easy as getting the result of the 3^{rd} or middle step of a 3 x 3 vertically and crosswise multiplication before any carry figure is added. (Note that it is easier to multiply polynomials that numbers because there are no “carries”)

The computations can be done mentally, using the coefficients:

- 2(x^2) x 6 = 12
- Plus 3(x) times – 4(x) = 0
- Plus -4 times 3(x^2) = -12

Only 3 multiplication and two addition steps are needed to get the correct answer.