What is the 6th term in the expansion of (3a^2 - 2b)^10(3a2−2b)10?

1 Answer
Noah G
Aug 24, 2016

t_6 = -1,959,552a^10b^5t6=−1,959,552a10b5

Explanation:

When finding specific terms in a binomial expansion, we need to use the formula T_(r + 1) = color(white)(two)_nC_r xx a^(n - r) xx b^rTr+1=twonCr×an−r×br, where tt is the term in the expansion of (a + b)^n(a+b)n.

Let's start by solving for rr.

r + 1 = 6 -> r = 5r+1=6→r=5

t_6 = color(white)(two)_10C_5 xx (3a^2)^5 xx (-2b)^5t6=two10C5×(3a2)5×(−2b)5

t_6 = -1,959,552a^10b^5t6=−1,959,552a10b5

Footnote:

The formula color(white)(two)_nC_rtwonCr represents (n!)/((n - r)!r!)n!(n−r)!r!, where ! ! is factorial. By definition, (n!)= n(n - 1)(n - 2)...(1).

Hopefully this helps!

Related questions
See all questions in Pascal's Triangle and Binomial Expansion
Impact of this question
4666 views around the world
You can reuse this answer
Creative Commons License