Which term of expansion of (x^4+4)^24 contains x^32

Answer 1

Hi Madelyne L.,

It's time to get creative on a problem like this! If you started to expand the actual polynomial all the way, you might rapidly go nuts keeping track of coefficients and powers. So be clever, substitute variables: x^4 = x', and recognize that this is just like (x'+4)^24, and you are looking for the x'^8 term. Because (x^4)^8 = x^32 , right?

This is more managable, you already have the binomial expansion coefficients formula, with factorials, right? You just plug that in for your appropriate x'^8 position. But remember to then convert the variable back from x' to x for stating your answer! (The numerical coefficient won't change).

This is a general technique; always try to reframe a problem back to a form that's easy to manipulate, solve, then "unframe" the answer.

--Cheers, --Mr. d.

Answer 2

Apply the binomial theorem. it should be the 17th term.