Binomial expansion by factorial

While we can use either Pascal’s triangle or the notation to find the coefficients in a binomial expansion, we can also use factorials directly.

This is useful if we have unknowns in the expression for or .

Finding a specific term using factorials

If we want to find , we can use this formula:

Prove that using factorials.

Finding multiple coefficients

Expand using factorials to find the coefficients

Find the first 3 terms of the expansion of using factorials to find the coefficients