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Binomial expansion

I can't seem to find any examples in any of the textbooks I have on how to answer these types of questions (ones in bold):

1.
a) Show that (1+2x)3=1+6x+12x2+8x3 (1+2x)^3 = 1 + 6x + 12x^2 + 8x^3
b) Find the values of x for which (1+2x)3=1+8x3 (1+2x)^3 = 1 + 8x^3


Or "find the independent term of x in the expansion..." type of questions

Does anyone know where I could find some examples/provide some examples or any youtube videos that may help?

Thanks a lot!
b) You need to make −6x=12x2-6x = 12x^2. Can you see why?
Reply 2
Avatar for IgorYakov
IgorYakov
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3
Original post by Mr M
b) You need to make −6x=12x2-6x = 12x^2. Can you see why?



Nope sorry
Reply 3
Avatar for TenOfThem
TenOfThem
18
Original post by IgorYakov
Nope sorry


Because that would make the bit from the first line that you do not want "go away"
Original post by IgorYakov
Nope sorry


I'm not having that. Stare at the question a bit longer and make use of the information I gave you.
Reply 5
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IgorYakov
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Original post by TenOfThem
Because that would make the bit from the first line that you do not want "go away"


Oh right, how do I make that? because If I put a value for X wouldn't they turn into numbers without x?
Reply 6
Avatar for IgorYakov
IgorYakov
OP
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Original post by Mr M
I'm not having that. Stare at the question a bit longer and make use of the information I gave you.



I thought that if we were supposed to cancel it we would need to make −6x−12x2 -6x - 12x^2 so I wasn't too sure
Original post by IgorYakov
I thought that if we were supposed to cancel it we would need to make −6x−12x2 -6x - 12x^2 so I wasn't too sure


I'm not really sure what you are saying.

You have been asked to find out which values of x make the following true:

1+6x+12x2+8x3=1+8x31+6x+12x^2+8x^3=1+8x^3

This means 6x+12x2=06x+12x^2=0

You can factorise this:

6x(1+2x)=06x(1+2x)=0

Which leads to two solutions.
Reply 8
Avatar for IgorYakov
IgorYakov
OP
3
Original post by Mr M
I'm not really sure what you are saying.

You have been asked to find out which values of x make the following true:

1+6x+12x2+8x3=1+8x31+6x+12x^2+8x^3=1+8x^3

This means 6x+12x2=06x+12x^2=0

You can factorise this:

6x(1+2x)=06x(1+2x)=0

Which leads to two solutions.


Aah right! I didn't think about that properly, sorry for that and thanks!!
Original post by IgorYakov
Aah right! I didn't think about that properly, sorry for that and thanks!!


No problem.
Reply 10
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IgorYakov
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3
Original post by Mr M
No problem.



Sorry last thing, that would give the solutions x = 0 and x = -1/2 right? the book says x = 0 and x = 1/2 not negative, is this right?
Original post by IgorYakov
Sorry last thing, that would give the solutions x = 0 and x = -1/2 right? the book says x = 0 and x = 1/2 not negative, is this right?


Try substituting the answer you are unsure about into the two expressions. Does it work?
Reply 12
Avatar for IgorYakov
IgorYakov
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3
Original post by Mr M
Try substituting the answer you are unsure about into the two expressions. Does it work?



Aah yeah, so it is -1/2 thanks!

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