I need help as to where I went wrong please! I will post the question as a comment where I can use the equation thing.

Question

anonymous · Answer

10. (i) Find the first three terms, in descending powers of x, in the expansion of $$( x - \frac{ 2 }{ x })^5$$
(ii) Hence find the coefficient of x in the expansion of $$(4 + \frac{ 1 }{ x^2 })(x - \frac{ 2 }{ x })^5$$

anonymous · Answer

I need help with (ii), I got the answers to the first part correct

anonymous · Answer

I multiplied the three terms from (i) by $$(4 + \frac{ 1 }{ x^2 })$$

anonymous · Answer

And I got 160 but the correct answer is 150, can you tell me what I did wrong?

whpalmer4 · Answer

First 3 terms in the expansion of (i) are
$$x^5-10x^3+40x$$right?
Multiply that by $$4+\frac{1}{x^2} = 4+x^{-2}$$
$$(4+x^{-2})(x^5-10x^3+40x) = 4(x^5-10x^3+40x)+x^{-2}(x^5-10x^3+40x)$$ignoring the terms that don't end up as $x$ terms:
$$4(40x)+x^{-2}(-10x^3) = 160x-10x^1=160x-10x = 150x$$ 
My guess is that you made a mistake when you multiplied $\frac{1}{x^2}*(-10x^3)$ or didn't collect like terms...

anonymous · Answer

Yes I made a mistake with multiplication I think, thank you very much!