Binomial Expansion

When the exponent is a positive integer:
( + )

When the exponent is negative or rational:
/
( 1 + )

Exercises for students
Solve the following problems on paper and check your expansions using the above application:

Expand (2x - 3y)4
Expand (2x - 3y)5
Expand (2x - 3y)6
Expand (1 + 2x)-1 as a series in ascending powers of x up to the term in x4
Expand (1 - 2x)-1 as a series in ascending powers of x up to the term in x4
Expand (1 - 2x)-2 as a series in ascending powers of x up to the term in x4
Expand (1 - 2x)-3 as a series in ascending powers of x up to the term in x4
Expand (1 - 3x)1/3 as a series in ascending powers of x up to the term in x3
Expand (1 - 3x)-1/3 as a series in ascending powers of x up to the term in x3
Expand (1 - 3x)1/2 as a series in ascending powers of x up to the term in x3
Expand (1 - 3x)2/3 as a series in ascending powers of x up to the term in x3
Expand (1 - 2x^2)-3 as a series in ascending powers of x up to the term in x6
Expand (1 + 1/x)-3 as a series in ascending powers of 1/x up to the term in 1/x3
Expand (1 + 1/x^2)-3 as a series in ascending powers of 1/x up to the term in 1/x6

Find the coefficient of t3 in the expansion of (2 - 5t)8 .

Express (1 - 3x)-1/2 as a series of ascending powers of x up to and including the term in x4 .