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Binomial Expansion

When expanding out a binomial for example: (2-3x)^5 ('^' indicating the indice)

Will it go to: 2^5 + (5C1)(2^4)(-3x)...

I get really confused as to if the indices go inside the brackets or outside of the brackets, can someone help please.
Reply 1
Avatar for Zacken
Zacken
22
Original post by lummzie
When expanding out a binomial for example: (2-3x)^5 ('^' indicating the indice)

Will it go to: 2^5 + (5C1)(2^4)(-3x)...

I get really confused as to if the indices go inside the brackets or outside of the brackets, can someone help please.


That's correct. The next term would be (5C2)(2^3)(-3x)^2 and NOT (5C2)(2^3)(-3^2 x) if that's what you're asking. So, really, the indices go outside the bracket, i.e: you raise the entire term to the exponent.
Reply 2
Avatar for lummzie
lummzie
OP
4
Original post by Zacken
That's correct. The next term would be (5C2)(2^3)(-3x)^2 and NOT (5C2)(2^3)(-3^2 x) if that's what you're asking. So, really, the indices go outside the bracket, i.e: you raise the entire term to the exponent.


Thank you so much, I now realise why I always get binomial wrong a lot its because I put (5C2)(2^3)(-3^2 x) instead of (5C2)(2^3)(-3x)^2. So then will the next be (5C3)(2^2)(-3X)^3 ?
Reply 3
Avatar for Zacken
Zacken
22
Original post by lummzie
Thank you so much, I now realise why I always get binomial wrong a lot its because I put (5C2)(2^3)(-3^2 x) instead of (5C2)(2^3)(-3x)^2. So then will the next be (5C3)(2^2)(-3X)^3 ?


Correct! :smile:
Reply 4
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lummzie
OP
4
Original post by Zacken
Correct! :smile:


So if I expanded (5C2)(2^3)(-3x)^2 would I expand this part (5C2)(2^3)(-3x) first and then square it?
Reply 5
Avatar for Zacken
Zacken
22
Original post by lummzie
So if I expanded (5C2)(2^3)(-3x)^2 would I expand this part (5C2)(2^3)(-3x) first and then square it?


Nopes, - to clarify, let me introduce more brackets, it should be:

(5C2) * (2^3) * ((-3x)^2) = (5C2) * (2^3) * ((-3x) * (-3x)) = (5C2) * (2^3) * (9x^)
Reply 6
Avatar for lummzie
lummzie
OP
4
Original post by Zacken
Nopes, - to clarify, let me introduce more brackets, it should be:

(5C2) * (2^3) * ((-3x)^2) = (5C2) * (2^3) * ((-3x) * (-3x)) = (5C2) * (2^3) * (9x^)


Okay thank you so much, this makes so much more sense now.
Reply 7
Avatar for Zacken
Zacken
22
Original post by lummzie
Okay thank you so much, this makes so much more sense now.


You're very welcome. :cool:

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