Question

Which term in the expansion of ((1/2x^3)-(x^5))^8 is a constant?

THANKS!!

Answer 1

It is a constant when the expansion has the term 1/2x^3 raised to the power of 5 and (x^5) raised to the power of 3. The product is x^0 which makes the term constant.

The term is:
-C(8,3) * (1/(2x^3))^5 * (x^5)^3
=-(8!/(3!5!)) * 1/(32x^15) * (x^15) )
=-(56/32)
=-7/4