what is equivalent to

(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

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