Q13/034) Multiplying Polynomials

Given two linear polynomials (a+bx) and (c+dx), their product is given by the quadratic polynomial
bd x² + (bc+ad) x + ac


Let this polynomial be represented by Ax² + Bx + C.
Thus A = bd, B=bc+ad, C = ac.

You are given the values of a,b,c,d and your task is to calculate the values of A,B,C. The constraint is that you can carry out only three multiplications.

solution

A = bd

B=bc+ad

C = ac.

 There are  4 multiplications

However if we convert B = (a+b)(c+d) – bd – ac = (a+b)(c+d) – A – C we have 3 multiplications