Extension 1 MAths ...plzzz help!!! (1 Viewer)

MAlame

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Topic: Bionomial Theorm

Question: Determine the term independent of x in the expansion

(1 - 3 x - 4 x^2 )( 1 + 2/x )^6 = 1 - 3x


thanks for any help :)
 

Mountain.Dew

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(1 - 3 x - 4 x^2 )( 1 + 2/x )^6 = 1 - 3x

well, you've got to get the constant terms - you need to find the right 'pairings' when you multiply the two binomial terms (the quadratic, and the one with power of 6) to get the independent terms.

So, with 1 --> pair up with 6
C0(1)^6
with - 3x --> pair up with
5C1(1)^5(2/x)
with -4x^2 --> pair up with
4C2(1)^4(2/x)^2

So, we get (1)(
6C0(1)^6) + (-3)(6C1(1)^5*(2) + (-4)(6C2(1)^4*(2)^2

= 1 + (-36) + (-240) = -275

And don't forget the 1 on the RHS...

so, the answer is -275-1 = -276.
 

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