Binomial expansion can be done quickly using the GC.

Consider binomial expansion of , where a is a real number, and q is a fraction or negative integer.

The recurrence formula for the coef works out to be

**Example 1**

Expand in ascending powers up to and including the term in

Using TI 84 Plus (OS 2.55)

Therefore, the expansion is

The recurrence formula can also be used to expand in descending powers of x.

**Example 2**

Expand in descending powers of x up to the 7th term.

Using TI 84 Plus (OS 2.55)

Therefore, the expansion is

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