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Help with Binomial Theorem! (1 Viewer)

Heresy

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This is question 15 from Exercise 5A from the Year 12 Volume of the Cambridge MX1 Textbook:

"Determine the value of the term independent of x in the expansion of: (1+2x)^4(1-1/x^2)^6"


Any help would be greatly appreciated! Thank you for your time!
 

HoldingOn

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This is question 15 from Exercise 5A from the Year 12 Volume of the Cambridge MX1 Textbook:

"Determine the value of the term independent of x in the expansion of: (1+2x)^4(1-1/x^2)^6"


Any help would be greatly appreciated! Thank you for your time!
For these questions just logically think about which terms in the expansion would multiply together to give a term in x^0 i.e. a constant term then add them together. In this case since the powers aren't that large write out the expansion of each and then do it that way. If they were bigger it would be best to do it in your head and just pick out the relevant terms.
 

pikachu975

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This is question 15 from Exercise 5A from the Year 12 Volume of the Cambridge MX1 Textbook:

"Determine the value of the term independent of x in the expansion of: (1+2x)^4(1-1/x^2)^6"


Any help would be greatly appreciated! Thank you for your time!
Powers in the first bracket range from 0 to 4 while in second bracket include 0, -2, -4, ..., -12

Hence to get a constant we can multiply both powers of 0 or a power of 2 and -2 or 4 and -4:

Constant term = 4C0x6C0 + 4C2(2x)^2*6C1(-1/x^2) + 4C4(2x)^4*6C2(-1/x^2)^2
= 1 - 144 + 240
= 97

Hope this is right haven't done binomial in a while!
 

Heresy

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Seconded Pika's answer.

I just expand the whole thing, (because i need to show working out -_-)
And have arrows to where they multiply to give desired power

Thank you so much!
 

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