SOLUTION: Not sure if this is the correct section, but here we go. From the book IB MYP 4, Haese, Second Edition, Chapter 4. Predict the simplification of (x - 1)(x^n + x^n-1+x^n-2+...x^2+

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Not sure if this is the correct section, but here we go. From the book IB MYP 4, Haese, Second Edition, Chapter 4. Predict the simplification of (x - 1)(x^n + x^n-1+x^n-2+...x^2+      Log On


   

Question 1102390: Not sure if this is the correct section, but here we go. From the book IB MYP 4, Haese, Second Edition, Chapter 4. Predict the simplification of (x - 1)(x^n + x^n-1+x^n-2+...x^2+x+1) where n E Z+
Answer by ikleyn(52817) About Me  (Show Source):
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(x - 1)*(x^n + x^n-1 + x^n-2 + . . . + x^2 + x + 1) = 


=        x^(n+1) + x^n + x^(n-1) + . . . + x^3 + x^2 + x - 

       -           x^n - x^(n-1) - . . . - x^3 - x^2 - x - 1 =         (after canceling all terms with opposite signs)
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=        x^(n+1) - 1.


Answer.   (x - 1)*(x^n + x^n-1 + x^n-2 + . . . + x^2 + x + 1) = = x^(n+1) - 1.