Is my text book messing wih me again?

[Styx]

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?

 

[cristo]

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]

 

[Styx]

Saved again, thanks Cristo

 

[cristo]

You're welcome.