CAS Binomial Theorem

[lacoste]

Is there a quick way to do these questions on the CAS with all the working out?

eg. expand (x+3)^4, then can the CAS show (n,r)....= (4,0)x^4 etc etc

[shinny]

There's no native function to show all the working out, but you could write a program which does this although it's not likely to even be worth the effort considering that there's unlikely to be any exam question which will require you to show the working out for a binomial expansion. If you're after just the answer, just use the 'expand(' command.

My advice is just to learn it properly since if it does come up in the non-calculator exam (and it's actually more likely to), then at least you'll know how to do it. Secondly, it's actually faster to just do it by hand straight off than having to enter it into the calculator and transcribe it back onto your exam paper.

[lacoste]

okay thanks.

when i use the bionomial theorem for (5x-2)^6 by hand i keep on getting the wrong answer for some reason.

is the first expansion by hand this: (6,0)5x^6    equals to 5x^6 but the answer is 15625x^6 +... ... other expansions

note: nCr=(n,r)

[TrueTears]

yeah you could also use pascals triangle, where the numbers of each row are actually the combination before the x values. So if you had a quadratic expressions you would look at the 3rd row, since a quadratic always has 3 terms (ax^2 + bx^1 + cx^0), and pascals triangle has 1 2 1 for the third row, so instead of working out the combinations, you would just read off the row XD                             

[lacoste]

cheers! Could someone please expand this with working out: (5x-2)^6

i've tried many times and keep getting the wrong answer.

[TrueTears]

So using the binomial expansion:

6C0 (5x)^6 (-2)^0 + 6C1 (5x)^5 (-2)^1 + 6C2 (5x)^4 (-2)^2 + 6C3 (5x)^3 (-2)^3 + 6C4 (5x)^2 (-2)^4 + 6C5 (5x)^1 (-2)^5 + 6C6 (5x)^0 (-2)^6

(Reading off a pascals triangle, or working out the Combinations seperately, or using a calc to work out the arithmetic) we get :

15625x^6 - 37500x^5 + 37500x^4 - 20000x^3 + 6000x^2 -960 x +64

[lacoste]

NEVER MIND, PROBLEM IS SOLVED!

THANKS !!

=] =]

[lacoste]

thanks true tears, when you just posted i worked it out myself.

i forgot to do the brackets for the coefficients.

thanks anyways man!!!!!!!!

[TrueTears]

haha , yeah it gets pretty messy after the power gets after 4, so gotta becareful XD

[lacoste]

is the binomial theorem when expanding larger powers eg (x+4)^6, only for the calculator exam by vcaa?

is there any binomial theorem in the NON-CALC exam?

cheers

[shinny]

is the binomial theorem when expanding larger powers eg (x+4)^6, only for the calculator exam by vcaa?

I'd assume so since it's just an unnecessary waste of time and all they really want is to ensure that you're able to apply the binomial theorem. In this case, I'd probably expect powers of 3 or 4 at most.

is there any binomial theorem in the NON-CALC exam?

I'm not too sure about in previous VCAA history, but I don't see why they couldn't put it in this year's exam. Especially considering that you're doing the CAS course, it's even more likely for them to test the binomial theorem in the non-calculator exam if they decide to test it at all (it's not something that's tested often).

[TrueTears]

hm, our teacher just said today that they probably won't give you higher than ^5, but who knows XD