SOLUTION: prove that (x-1)(x^8+x^7+x^6+...+1)=x^9-1 without multiplying out the brackets.

Algebra ->  Square-cubic-other-roots -> SOLUTION: prove that (x-1)(x^8+x^7+x^6+...+1)=x^9-1 without multiplying out the brackets.      Log On


   

Question 842116: prove that (x-1)(x^8+x^7+x^6+...+1)=x^9-1 without multiplying out the brackets.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Look at the first two terms.
%28x-1%29x%5E8%2B%28x-1%29x%5E7=x%5E9-x%5E8%2Bx%5E8-x%5E7=x%5E9-x%5E7
The two terms sum to remove all but the first and last terms.
Similarly when you complete the multiplication, all that will be left are
(x^9-x^8+x^8+x^7-x^7+...-x+x-1)
%28x-1%29%28x%5E8%2Bx%5E7%2Bx%5E6%2Bx%5E5%2Bx%5E4%2Bx%5E3%2Bx%5E2%2B1%29=x%5E9-1