Combinations and Permutations Question

[snaidu228]

Homework Statement

1) What is the coefficient of x^43 in the expansion of [(2/x^2) − x3)^16?
(2) What is the coefficient of x^14y^12 in the expansion of (3x − 2y)^26?

Homework Equations

Binomial Expansion

The Attempt at a Solution

For (1),

I started out like this:

(16 0) ( 2/x^2)^16 (-x^3)^0 + (16 1) (2/x^2)^15 (-x^3)^1 +...+ (16 16) (2/x^2)^0 (-x^3)^16.

Is that how we do it?
Do we do the same for (2)?

 

[tiny-tim]

Hi snaidu228!

(try using the X² tag just above the Reply box )

I started out like this:

(16 0) ( 2/x^2)^16 (-x^3)^0 + (16 1) (2/x^2)^15 (-x^3)^1 +...+ (16 16) (2/x^2)^0 (-x^3)^16.

Is that how we do it?

Yes, that's it (except, of course, you only need the one term that has x⁴³).

(and similarly for (2))

 

[snaidu228]

Thank you very much!