Binomial expansion

[young sedge]

I tried getting the general term for multiplication and representing each r as an arthimatic sequence but it didn't work, any help would be appreciated

[river topaz]

its a geometric progression

you can simplify them by its sum formula, replace them with formula and check if that helps

[fringe bay]

Don't know if this is correct but here a start ( if we can say that : I often forget Formula's that I don't often use here is a kind of alternative)

But if you have the formula it would be better to use it ig

[tidal hollow]

,rccw

[violet crystal]

.solved