SOLUTION: Without expanding, find the coefficient of x^3 in the normal form of each polynomial. 1. (x-1)(x^6+x^5+x^4+x^3+x^2+x+1)

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Without expanding, find the coefficient of x^3 in the normal form of each polynomial. 1. (x-1)(x^6+x^5+x^4+x^3+x^2+x+1)      Log On


   

Question 1177629: Without expanding, find the coefficient of x^3 in the normal form of
each polynomial.
1. (x-1)(x^6+x^5+x^4+x^3+x^2+x+1)
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
Performing the multiplication and combine like-terms!

Answer by ikleyn(52824) About Me  (Show Source):
You can put this solution on YOUR website!
.

(x-1)*(x^6+x^5+x^4+x^3+x^2+x+1) = x^7 - 1.


This formula is the closest relative of the well known formula for the sum of the first 7 terms of an geometric progression.