Use the Binomial Theorem to find the binomial expansion of the expression. (d+3)^7

Question

anonymous · Answer

@amistre64

amistre64 · Answer

might help to determne what the thrm states

anonymous · Answer

huh? o.o

amistre64 · Answer

(p+q)^n = $\Large \sum_{r=0}^{n}\binom{n}{r}~p^nq^{...}$
forgot the q part

amistre64 · Answer

you are being asked to apply a thrm, so it would be best to know the thrm.  the rest is just filling in the specifics

amistre64 · Answer

r+n, and r

amistre64 · Answer

$$\Large \sum_{r=0}^{n}\binom{n}{r}~p^{n-r}~q^{r}$$

anonymous · Answer

oh okay.. I'm just stuck on which one is right..d7 + 21d6 + 189d5 + 945d4 + 2835d3 + 5103d2 + 5103d + 2187 or d7 + 7d6 + 21d5 + 35d4 + 35d3 + 20d2 + 7d + 1..

amistre64 · Answer

i believe the 21, 35  stuff is if q=1

amistre64 · Answer

1 7 21 35 35 21 7 1  is a direct line from pascals triangle, which would represent q=1 in this case

anonymous · Answer

.-. but these are the options i have.. -bit confused-

anonymous · Answer

Ohh ok

amistre64 · Answer

and what is the difference between the options?  the coeffs of each term.

in the setup (p+1)^7 , the coeffs follow pascals triangle:  1 7 21 35 ...

notice that your problem has q=3, not q=1.  so which one of these options would we choose?