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Is my text book messing wih me again?

  • Thread starter Styx
  • Start date
  • #1
27
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Here is an example in my book...

Determine the coefficient of x^6 in the expansion of

(2-3x^2)(1+2x)^8


(2-3x^2)(1+2x)^8 = 2(1+2x)^8 - 3x^2(1+2x)^8

The general term in the expansion of (1+2x)^8 is

C(8,k)(2x)^k

Therefore, the term containing x^6 in the expansion of (2-3x^2)(1+2x)^8 is

2(C(8,6))(2x)^6 - 3x^2(C(8,4))(2x)^4 = 2(2^6)(C(8,6))(x^6) - 3(2^4)(C(8,4))(x^6) = 224x^6

The coefficient is 244

Where the heck did these 4's come from??? Shouldn't they be 6's or am I missing something?
 
Last edited:

Answers and Replies

  • #2
cristo
Staff Emeritus
Science Advisor
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You're looking for the coefficient of x^6. In the first term, this will be equal to the coefficient of x^6, but the second term is premultiplied by x^2, thus to obtain the coefficient of x^6 in this term, you must look at the term x^4 in the expansion of (1+2x)^8 [since x^2.x^4=x^6]
 
  • #3
27
0
Saved again, thanks Cristo
 
  • #4
cristo
Staff Emeritus
Science Advisor
8,107
72
You're welcome.
 

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