Find the coefficient of x^2 in the expansion of [2x-(1/2x)]^6

Question

In the expansion of the equation, find the coefficient of x^2. 

Answer 1

By the Binomial Theorem, [2x-(1/2x)]^6 can be expanded to the sum as k goes from zero to 6 of (6 choose k)×(2x)^k×(-1/2x)^6-k.   The only time we will be left with an x² term is when k=4, since we'll have some coefficient multiplied by x⁴/x².  So, we'll have (6 choose 4) × (2x)⁴×(-1/2x)², which is 15×16x⁴×(1/4x²)= 60x².

 

So the coefficient is 60.