Let p and q be polynomials (maybe in several variables, over a field), and suppose they have m and n non-zero terms respectively. We can assume m≤n. Can it ever happen that the product p⋅q has fewer than m non-zero terms?

I ask this because I vaguely recall seeing a positive answer in book somewhere (probably about computation or algorithms since the polynomials were unwieldy). If anyone knows what book this is from it would be much appreciated.

**Answer**

(x2−2x+2)(x2+2x+2)=x4+4.

**Attribution***Source : Link , Question Author : Chris Brooks , Answer Author : André Nicolas*