Expand the following:
(1 - p) (p^6 + p^5 + p^4 + p^3 + p^2 - p^1 + 1)
| | | | | | | | | | | | -p | + | 1
| | p^6 | + | p^5 | + | p^4 | + | p^3 | + | p^2 | - | p | + | 1
| | | | | | | | | | | | -p | + | 1
| | | | | | | | | | p^2 | - | p | + | 0
| | | | | | | | -p^3 | + | p^2 | + | 0 | + | 0
| | | | | | -p^4 | + | p^3 | + | 0 | + | 0 | + | 0
| | | | -p^5 | + | p^4 | + | 0 | + | 0 | + | 0 | + | 0
| | -p^6 | + | p^5 | + | 0 | + | 0 | + | 0 | + | 0 | + | 0
-p^7 | + | p^6 | + | 0 | + | 0 | + | 0 | + | 0 | + | 0 | + | 0
-p^7 | + | 0 | + | 0 | + | 0 | + | 0 | + | 2 p^2 | - | 2 p | + | 1:
-p^7 + 2 p^2 - 2 p + 1
+895 I'm not sure. I did it differently. I took (1-p) and distributed it into (1-p1+p2+p3+p4+p5+p6).
I got: \((1-p^1+p^2+p^3+p^4+p^5+p^6)+(-p^1+p^2-p^3-p^4-p^5-p^6-p^7)\)
This is the same as: \(1-p^1+p^2+p^3+p^4+p^5+p^6+-p^1+p^2-p^3-p^4-p^5-p^6-p^7\)
I just used parenthesis for clarity.
I then combined like terms.
\(1-2p^1+2p^2-p^7\)
2p1 is the same as 2p.
1-2p+2p2-p7
