Question

The binomial theorem, how do I use it?
\[(x+y)^n = \sum_{k=0}^n \binom{n}{k}x^{n-k}y^k.\]
Now how do I use that crazy theorem for a binomial like this:
\[(d – 5y)^6\]

Answer 1

let x = d , let y = -5y, let n = 6

Answer 2

\[(d-5y)^n = \sum_{k=0}^6 \binom{6}{k}d^{6-k}-5y^k.\]
Okay, where do I go from there?

Answer 3

if you have to list all the terms, then its just a matter of letting k=0, then k=1, then k=2, then ... till k=6; and you should have -5y wrapped up as a single term

\[(d-5y)^n = \sum_{k=0}^6 \binom{6}{k}d^{6-k}(-5y)^k\]
\[\binom{6}{0}d^{6-0}(-5y)^0+\sum_{k=1}^6 \binom{6}{k}d^{6-k}(-5y)^k\]

\[\binom{6}{0}d^{6-0}(-5y)^0+\binom{6}{1}d^{6-1}(-5y)^1+\sum_{k=2}^6 \binom{6}{k}d^{6-k}(-5y)^k\]
etc ...

Answer 4

Thanks I understand now :-).

Answer 5

youre welcome ... its just a pain to do, simple enough lol, but a pain