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Binomial Expansion

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1. 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.
2. (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.
3. (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 ?
4. (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!
5. (Original post by Zacken)
Correct!
So if I expanded (5C2)(2^3)(-3x)^2 would I expand this part (5C2)(2^3)(-3x) first and then square it?
6. (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^)
7. (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.
8. (Original post by lummzie)
Okay thank you so much, this makes so much more sense now.
You're very welcome.

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