Binomial expansion (1 Viewer)

[swagswagyoloswag]

Is this always the way you expand it? Because I was doing a question where their general term was:

The powers are swapped around. Although it is symmetrical, this is not correct right? Because it's like I'm reading it right to left.
The answer differed from mine because they had swapped their powers around and Im not sure which is correct
The specific question was:





.

 

[VBN2470]

Since swapping the x with y doesn't change anything, as long as it is consistent it should work. Based on what the general term is, try to find which variable goes first and which one goes second manipulate your expression from there.

 

[braintic]

Is this always the way you expand it? Because I was doing a question where their general term was:

The powers are swapped around. Although it is symmetrical, this is not correct right? Because it's like I'm reading it right to left.
The answer differed from mine because they had swapped their powers around and Im not sure which is correct
The specific question was:




.

They are both correct. A general term is simply one that can be used to generate any term in the sequence, and both do that.

4r/3 can't be correct - it leads to non-integer powers.

 

[swagswagyoloswag]

They are both correct. A general term is simply one that can be used to generate any term in the sequence, and both do that.

4r/3 can't be correct - it leads to non-integer powers.

But if n = 4r, and n = 12 (which was in part (i)), then r = 3. the term is 12C3 (2x^3)^9 (-1/x)^3 which isn't constant

 

[braintic]

But if n = 4r, and n = 12 (which was in part (i)), then r = 3. the term is 12C3 (2x^3)^9 (-1/x)^3 which isn't constant

The r in their answer is not the r in the general term formula. I'm guessing they used a different pronumeral in the general term, like k.

Assuming it was k, instead of saying n=4k/3, you should be saying k=3n/4.
This has to be an integer, and that only happens when n is a multiple of 4, ie. n=4r where r is any integer

 

[swagswagyoloswag]

The r in their answer is not the r in the general term formula. I'm guessing they used a different pronumeral in the general term, like k.

Assuming it was k, instead of saying n=4k/3, you should be saying k=3n/4.
This has to be an integer, and that only happens when n is a multiple of 4, ie. n=4r where r is any integer

So was I wrong? Im confused. If i expanded like the way I did in the exam and got a fraction, should I reverse the powers too?

 

[braintic]

So was I wrong? Im confused. If i expanded like the way I did in the exam and got a fraction, should I reverse the powers too?

No you were right. They would have got exactly what you did. You just misinterpreted your answer, and didn't finish it off.

 

[swagswagyoloswag]

No you were right. They would have got exactly what you did. You just misinterpreted your answer, and didn't finish it off.

Makes a lot of sense, thanks. Also, about the swapping of powers, what if they ask for the 5th term (T5)? This would depend on where I put the powers [ 'n-r' and 'r' ] wouldnt it? Which case is correct?

 

[braintic]

Makes a lot of sense, thanks. Also, about the swapping of powers, what if they ask for the 5th term (T5)? This would depend on where I put the powers [ 'n-r' and 'r' ] wouldnt it? Which case is correct?

There has never been such a question in an HSC exam, due to the ambiguity.
They only ask for the coefficient of something, such as the coefficient of x^3. There is no ambiguity then, and each method gives the same answer.