what is equivalent to

Question

(1-p)(1 + p + p^2 +p^3+ p^4 + p^5 + p^6)

Is there any way to do this quickly without distributing? If so, how or what is the best way to distribute? Thanx

Answer 1

Somewhere along your studies in math you might come across the factor pattern of ..
for any 1 - x^n , where n is odd, 1 - x is a factor and we get
1 - x^n = (1-x)(1 + x + x^2 + x^3 + ... + x^(n-1) ) , so

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