How do you use the binomial theorem to expand #(u^(3/5)+2)^5#?

1 Answer
Oct 20, 2017

Answer:

See below.

Explanation:

#((5),(0))(u^(5/3))^5*2^0+((5),(1))(u^(5/3))^4*2^1+((5),(2))(u^(5/3))^3*2^2 ->+((5),(3))(u^(5/3))^2*2^3+((5),(4))(u^(5/3))^1*2^4+((5),(5))(u^(5/3))^0*2^5#

#u^(25/3)+10u^(20/3)+40u^5+80u^(10/3)+80u^(5/3)+32#

As can be seen the exponent of the first term decreases from n to 0 and at the same time the exponent of the second term increases from 0 to n.

#((n),(r))# is called the binomial coefficient and is the number of
combinations of n things taken r at a time. This can also be expressed as #n C r#