Need help with Binomial expansion urgently!

could someone please help me with the following question (exam style question),and explain in full how to do it?
thanks in advance.

For the binomial expansion, in descending powers of x, of (x^3 - 1/2x)^12
( just to clarify the '2' is the coefficient of x in this case if it seemed unclear).

(1) find the first 4 terms simplifying each term.
(2) find in its simplest form the term independent of x in this expansion.

( also could you please check if this expansion of (a+b)^12 is correct?)
a^12+12a^11+b+66a^10b^2+220a^9b^3.....…

Since you say '2' is coefficient of x (as opposed to 1/2),
then I assume that all of 2x is in denominator.
If so, you MUST use parentheses: (x^3 - 1/(2x))^12

First 4 terms:

(12C0) (x³)¹² (−1/(2x))⁰ + (12C1) (x³)¹¹ (−1/(2x))¹ + (12C2) (x³)¹⁰ (−1/(2x))² + (12C3) (x³)⁹ (−1/(2x))³
= 1 x³⁶ + 12 x³³ (−1/(2x)) + 66 x³⁰ (1/(4x²)) + 220 x²⁷ (−1/(8x³))
= x³⁶ − 6 x³² + 33/2 x²⁸ − 55/2 x²⁴

Constant term:

nth term = (12Cn) (x³)^(12-n) (−1/(2x))^n

We need to find n so that coefficient of x = 0
3(12−n) + (-1)n
36 − 3n − n = 0
36 = 4n
n = 9

(12C9) (x³)³ (−1/(2x))⁹
= 220 x⁹ (−1/(512x⁹))
= −220/512
= −55/128

------------------------------

Thanks for Additional Info

Your expansion of (a+b)^12 got truncated (you need to include spaces
or else Y!A truncates anything that is longer than about 35 characters.

Here's a link where you can check:
http://www.wolframalpha.com/input/?i=exp…

I will assume that you mean (x^3 - 1/(2x))^12.

(1) The first four terms are

12C0(x^3)^12 (-1/(2x))^0 + 12C1(x^3)^11 (-1/(2x))^1 + 12C2(x^3)^10 (-1/(2x))^2
+ 12C3(x^3)^9 (-1/(2x))^3

= x^36 - 6x^32 + (33/2)x^28 - (55/2)x^24.

(2) We need a term of the form 12Cn(x^3)^(12-n) (-1/(2x))^n so that the overall exponent on x is zero.
The overall exponent on x is 3(12 - n) - n.
3(12 - n) - n = 0; 36 - 3n - n = 0; 36 = 4n; n = 9.

So the term independent of x is
12C9(x^3)^3 (-1/(2x))^9 = 220x^9 (-1/(512x^9)) = -55/128.

(3) For (a + b)^12, you almost started off correctly, except there should not be a + sign between the 12a^11 and the b.
I see that you tried again to expand (a + b)^12, and this time you did it perfectly! Nice job!

Lord bless you today!

( also could you please check if this expansion of (a+b)^12 is correct?)
a^12+12a^11+b+66a^10b^2+220a^9b^3.....…

you have a (probably) typo in your second term...12a^11 b...

your expansion is not completed !

one problem at a time.

@ß