Question

7
(i)Find the first three terms, in ascending powers of x, in the expansion (1-2x)^6.
Answer: 1-12x+60x^2
(ii) Hence find the the coefficients of x and x^2 in the expansion of (4-x)(2-4x)^6.
This is the one I nee help with please! I tried this:
(4-x)(1-12x+60x^2) but that really got me a very wrong answer.

Answer 1

(4-x)\[(2-4x)^{6}\] =(4-x)[ \[2^{6}-6\times2 ^{5}\times4x +15\times2 ^{4}\times \left( 4x \right) ^{2} +....+\left( 4x \right)^{6}]\]
A)coefficient of x = \[4\times6\times2 ^{5}\times4-2^{6} =2^{5}\left( 4\times6\times4-2 \right)=32\times94=3008\]

Answer 2

B) coefficient of \[x^{2}=4\times15\times2 ^{4}\times4 ^{2}-6\times 2^{5}\times4\]
simplipy it you will get the answer

Answer 3

I actually don't really understand what you did there, sorry! Could you go into some more detail please?

Answer 4

\[(4-x)(1-12x+60x^2+\cdots) \]

all the components thats comes in the dots has x with a degree greater than 2
so after multiplication with (4-x) non of those component will give out a \(x\) or a \(x^2\) term

Answer 5

so expand the expression that ive given and group the \(x\) and \(x^2\) terms like dayakar did

Answer 6

Yeah but when i do that I get -54x and 252x^2 which is no where near right

Answer 7

Should I post a picture of the working out?

Answer 8

oh and forgot,

the first answer is given for expansion of \((1-2x)^6\) but the part asks for \((2-4x)^6\)

so \((2-4x)^6 = [2(1-2x)^6]= 2^6 (1-2x)^6 = (2^6-12\times2^6 x+2^6\times 60x^2+ \cdots)\\ = (64-768x+3840x^2+\cdots)\)

Answer 9

Ooh I didnt notice that..

Answer 10

Aha! Getting the right thing now, thank you very much!