A)
Using the Binomial Theorem:

Then, replace for a=3x⁵, b=-1/9 y³ and n=4 to find the summation notation that Harold uses to express the expansion:

B)
To find the simplified terms of the expansion, expand the sum using the corresponding values of k from 0 to 4:

Simplify the exponents of the parentheses (3x^5):

Simplify the binomial coefficients:

Elevate each parenthesis to its corresponding power:

Next, multiply all the factors on each term:

Finally, simplify all the coefficients:

Therefore, the simplified terms of the expansion are:
