165k views
4 votes
Find the middle team and team independent x in the expansion of (3 -2x)^8​

1 Answer

4 votes

Answer:

We can find the middle term and the term independent of x in the expansion of (3 - 2x)^8 using the Binomial Theorem.

The general term in the expansion of (3 - 2x)^8 is given by:

T(r+1) = C(8, r)(3)^(8-r)(-2x)^r

where C(8, r) is the number of combinations of 8 things taken r at a time, or 8!/[r!(8-r)!].

The middle term occurs when r = 4 (since there are 8 terms in the expansion). So the middle term is:

T(5) = C(8, 4)(3)^4(-2x)^4 = 1683 * 81 * 16x^4 = 5515476x^4

The term independent of x occurs when r = 0. So the term independent of x is:

T(1) = C(8, 0)(3)^8(-2x)^0 = 6561

Therefore, the middle term is 5515476x^4, and the term independent of x is 6561.

User Jakx
by
8.7k points

No related questions found