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

[MAlame]

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

 

[Pastafarian]

Err isn't it one?

 

[Mountain.Dew]

(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 ⁶C₀(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.