SOLUTION: Please help me use the binomial theorem to expand this expression {{{(2-x)^5}}} I know how to get the answer from the calculator, but I dont know how to get this expression into

Algebra ->  Sequences-and-series -> SOLUTION: Please help me use the binomial theorem to expand this expression {{{(2-x)^5}}} I know how to get the answer from the calculator, but I dont know how to get this expression into      Log On


   



Question 326188: Please help me use the binomial theorem to expand this expression %282-x%29%5E5
I know how to get the answer from the calculator, but I dont know how to get this expression into the calculator form.

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!


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)

------------------------------------------- 


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

%282-x%29%5E5

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

1st term:  %285C0%29%282%29%5E5%28-x%29%5E0

2nd term:  %285C1%29%282%29%5E4%28-x%29%5E1

3rd term:  %285C2%29%282%29%5E3%28-x%29%5E2

4th term:  %285C3%29%282%29%5E2%28-x%29%5E3

5th term:  %285C4%29%282%29%5E1%28-x%29%5E4

6th term:  %285C5%29%282%29%5E0%28-x%29%5E5

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

Simplifying 1st term:

%285C0%29%282%29%5E5%28-x%29%5E0%22%22=%22%22%281%29%2832%29%281%29%22%22=%22%2232

Simplifying 2nd term:

%285C1%29%282%29%5E4%28-x%29%5E1%22%22=%22%22%285%29%2816%29%28-x%29%22%22=%22%22-80x

Simplifying 3rd term:

%285C2%29%282%29%5E3%28-x%29%5E2%22%22=%22%22%2810%29%288%29%28x%5E2%29%22%22=%22%2280x%5E2

Simplifying 4th term:

%285C3%29%282%29%5E2%28-x%29%5E3%22%22=%22%22%2810%29%284%29%28-x%5E3%29%22%22=%22%22-40x%5E3

Simplifying 5th term:

%285C4%29%282%29%5E1%28-x%29%5E4%22%22=%22%22%285%29%282%29%28x%5E4%29%22%22=%22%2210x%5E4

Simplifying 6th term:

%285C5%29%282%29%5E0%28-x%29%5E5%22%22=%22%22%281%29%281%29%28-x%5E5%29%22%22=%22%22-x%5E5

So:

%282-x%29%5E5%22%22=%22%2232%22%22-%22%2280x%22%22%2B%22%2280x%5E2%22%22-%22%2240x%5E3%22%22%2B%22%2210x%5E4%22%22-%22%22x%5E5

Edwin