Question 326188
<pre><b>

You only need to be able to get {{{nCr}}} on your calculator.
On the TI-84, suppose you wanted, say for example, 9C3

On the cleared main screen, type the value of n (in this example 9)
Press MATH
Press the left arrow
Press 3
type the value of r (in this example 3)
You should see -->  9 nCr 3
Press ENTER
             (in this example you get 84)

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Now we'll set up the terms of the binomial expansion for:

{{{(2-x)^5}}}

There is always one more term than the exponent.  The
emponet is 5.  So there are 6 terms:

1st term:  {{{(5C0)(2)^5(-x)^0}}}

2nd term:  {{{(5C1)(2)^4(-x)^1}}}

3rd term:  {{{(5C2)(2)^3(-x)^2}}}

4th term:  {{{(5C3)(2)^2(-x)^3}}}

5th term:  {{{(5C4)(2)^1(-x)^4}}}

6th term:  {{{(5C5)(2)^0(-x)^5}}}

Observe that pattern carefully so you can do other
binomial expansion problems.

Simplifying 1st term:

{{{(5C0)(2)^5(-x)^0}}}{{{""=""}}}{{{(1)(32)(1)}}}{{{""=""}}}{{{32}}}

Simplifying 2nd term:

{{{(5C1)(2)^4(-x)^1}}}{{{""=""}}}{{{(5)(16)(-x)}}}{{{""=""}}}{{{-80x}}}

Simplifying 3rd term:

{{{(5C2)(2)^3(-x)^2}}}{{{""=""}}}{{{(10)(8)(x^2)}}}{{{""=""}}}{{{80x^2}}}

Simplifying 4th term:

{{{(5C3)(2)^2(-x)^3}}}{{{""=""}}}{{{(10)(4)(-x^3)}}}{{{""=""}}}{{{-40x^3}}}

Simplifying 5th term:

{{{(5C4)(2)^1(-x)^4}}}{{{""=""}}}{{{(5)(2)(x^4)}}}{{{""=""}}}{{{10x^4}}}

Simplifying 6th term:

{{{(5C5)(2)^0(-x)^5}}}{{{""=""}}}{{{(1)(1)(-x^5)}}}{{{""=""}}}{{{-x^5}}}

So:

{{{(2-x)^5}}}{{{""=""}}}{{{32}}}{{{""-""}}}{{{80x}}}{{{""+""}}}{{{80x^2}}}{{{""-""}}}{{{40x^3}}}{{{""+""}}}{{{10x^4}}}{{{""-""}}}{{{x^5}}}

Edwin</pre>