Expert: Paul Klarreich - 2/4/2011

Question
Hi...I need help with the following question:

" Show how to use Pascal's triangle to expand (x + 2)^4 by reproducing the relevant rows of the triangle. "

Answer
Questioner: Trish
Country: Canada
Category: Advanced Math
Private: No
Subject: Pascal's Triangle - Help!
Question: Hi...I need help with the following question:

" Show how to use Pascal's triangle to expand (x + 2)^4 by reproducing the relevant rows of the triangle. "
.......................................

I: Write the P.T. down to level 4:  

-- you will have coefficients like  1   3   3   1  (for n=3; I leave n=4 for you; why should I have all the fun?)

II. In (a + b)^3 you would have  1  3  3  1, and they mean;

1*a^3 + 3*a^2b^1  + 3a^1b^2 + 1*b^3

Then you would change it to (x + 2)^4 by:

a. doing it for level 4 -- I assume you know WHAT P's T is --
b. replacing the a's with x's
c. replacing the b's with 2's and doing the arithmetic.

For example, the third term of (x + 2)^3 would take

+ 3a^1b^2 -->  + 3x^1(2)^2 = 12x

Your turn now.