Question

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

Answer 1

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`