Generally speaking, if you are adding terms, each of which is a polynomial degree N, then the sum is a polynomial of degree N+1. Here each term is of degree 2 so the sum is a polynomial of degree 3: . When n= 1, the sum is 1 so a+ b+ c+ d= 1. When n= 2, the sum is 1+ 4= 5 so 8a+ 4b+ 2c+ d= 5. When n= 3, the sum is 1+ 4+ 9= 14 so 27a+ 9b+ c+ d= 14. Finally, when n= 4, the sum is 1+ 4+ 9+ 16= 30 so 64a+ 16b+ 4c+ d= 30. Solve those 4 equations for a, b, c, d.