Complex distributing problem

[NotAnUnusualGuy]

I will admit that this problem simply a distributive property, but it's a bit more complex.
This is part of a computer science class, and I need this taken off my mind so that i can focus on other aspects of the problem.
Given that:
Note: the numbers that follow the letters are SUBSCRIPTS. The numbers are NOT powers.
I wanted to clarify this since it may be against the norm.

C1=G0+(P0*C0)
C2=G1+(P1*C1)
C3=G2+(P2*C2)
.
.
.
G7=G6+(P6*C6)

My question is:
What is the full expansion for C6 & C7?
I'm stuck on C5. So far I have G4 done.
C4 = G3 + P3*G2 + P3*P2*G1 + P3*P2*P1*G0 + P3*P2*P1*P0*C0
As I said before, there's more that I have to do with this expression after expanding it. The expansion itself is tiring.
For those wondering what part of computer science is for, we're studying carry-lookahead adders.

With this post, I'm going to sleep.

 

[HallsofIvy]

Looking at
C4 = G3 + P3*G2 + P3*P2*G1 + P3*P2*P1*G0 + P3*P2*P1*P0*C0
it looks like you have a clear pattern. I would say that
C6= G5+ P5*G4+ P5*P4*G3+ P5*P4*P3*G2+ P5*P4*P3*P2*G1+ P5*P4*P3*P2*P1*G0+ P5*P4*P3*P2*P1*P0*C0
and
C7= G6+ P6*G5+ P6*P5*G4+ P6*P5*P4*G3+ P6*P5*P4*P3*G2+ P6*P5*P4*P3*P2*G1+ P6*P5*P4*P3*P2*P1*G0+ P6*P5*P4*P3*P2*P1*P9*C0.

 

[NotAnUnusualGuy]

Thank you very much!