Expert: Sherry Wallin - 2/8/2011

Question
Hi, I need some help with this question:

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

Any help clarifying the route to show an accurate Pascal's triangle would be greatly appreciated.

Answer
TB~

Do you know what Pascal's Triangle looks like or how it is found?
The first row is for (a+b)^0 = 1; the 2nd row is for (a+b)^1 =
1*a+1*b; the 3rd row is for (a+b)^2 = 1*a^2+2ab+1*b^2 etc...
          1
       1   1
    1    2    1
  1   3    3    1
1  4    6    4    1
     ....

So you want to look at the 5th row for the coefficients on
(x+2)^4 = 1*x^4 + 4*x^3*2 + 6*x^2*2^2 + 4*x*2^3 + 1*2^4
= x^4 + 8x^3 + 24x^2 + 32x + 16

If you want to make sure this is correct rewrite (x+2)^4 as
(x+2)^2(x+2)^2 = (x^2 + 4x + 4)(x^2 + 4x + 4)
= x^4 + 8x^3 + 24x^2 + 32x + 16  Yep it is the same

Math Prof