# Polynomial Expansion Using Pascals Triangle

• May 3rd 2008, 08:24 AM
nugiboy
Polynomial Expansion Using Pascals Triangle
Heres the question followed by the textbook answer from the back.

http://i137.photobucket.com/albums/q220/e3tiger/NCR.jpg

Im stuck on how it got the answer. Ive just done about 5 others in the same way, but this one doesn't seem to give me the right answer.

I got:

$\displaystyle 1+12x+30x^2+40x^3+30x^4+12x^5+2x^6$

I did the correct method i think.
Heres the row of the pascal triangle i used:

1 6 15 20 15 6 1

So i basicly did:

$\displaystyle (1)(1^6)(2x^0) + (6)(1^5)(2x^1) + (15)(1^4)(2x^2)$... etc and simplified. I really don't understand how i got the answer wrong. Any suggestions?
• May 3rd 2008, 08:28 AM
Moo
Hello,

Quote:

Originally Posted by nugiboy
Heres the question followed by the textbook answer from the back.

http://i137.photobucket.com/albums/q220/e3tiger/NCR.jpg

Im stuck on how it got the answer. Ive just done about 5 others in the same way, but this one doesn't seem to give me the right answer.

I got:

$\displaystyle 1+12x+30x^2+40x^3+30x^4+12x^5+2x^6$

I did the correct method i think.
Heres the row of the pascal triangle i used:

1 6 15 20 15 6 1

So i basicly did:

$\displaystyle (1)(1^6)({\color{red}(}2x{\color{red})}^0) + (6)(1^5)({\color{red}(}2x{\color{red})}^1) + (15)(1^4)({\color{red}(}2x{\color{red})}^2)$... etc and simplified. I really don't understand how i got the answer wrong. Any suggestions?

The mistakes are in red ;)
• May 3rd 2008, 08:29 AM
james_bond
Remember that it is $\displaystyle \left(1+\left(2x\right)\right)^6$!