Question

what is the fifth term of (a-3b)^5

Answer 1

row 5: 1 5 10 10 5 1
fifth term is 5*(a)*(-3b)^4

Answer 2

can you simplify from there? (the way i got this: pascal's triangle: http://ptri1.tripod.com/ptreal1r.gif)

Answer 3

another way to see it:
the expansion of a binomial is to a natural exponent is given by\[(x+y)^n=\sum_{k=0}^n\binom nkx^{n-k}y^k\]where \[\binom nk={n!\over k!(n-k)!}\]so the \((k+1)^{th}\) therm of a binomial expansion is given by \[\binom nkx^{n-k}y^k\]

Answer 4

Yep. That's another option, actually it's better to use that because you're not always going to have access to pascal's triangle, or the time to draw it out (:

Answer 5

it may be a bit more advanced than pascal's triangle, but as you noticed it's more powerful (because it's more general)

so if you can work with it, I would recommend it

Answer 6

k = the term # - 1, right?
So then
^That is how you would do it in this problem