Algebra 2 Pascal's Triangle?

(0th row)..............................1...............................................

(1st row ) .....................1 ............1 .....................................

(2nd row ................1............2 .............1................................

(3rd row ) .........1..........3 ............3 .............1 .......................

keep going until you get to the row you want.

The coefficients come from the 8th row of Pascal's triangle. If you don't want to write it out, you can compute it as follows:

C(8,0) = 8! / 8! 0! = 1

C(8,1) = 8! / 7! 1! = 8

C(8,2) = 8! / 6! 2! = 28

etc.

C(8,7) = 8! / 1! 7! = same as C(8,1) = 8

C(8,8) = 8! / 0! 8! = same as C(8,0) = 1

Then the terms will go from x^8, x^7y, x^6y^2, etc. Each time you decrement the exponent on x, but increment the exponent on y until you get to y^8.

The final expansion of (x + y)^8 will be:

x^8 + 8x^7y + 28x^6y^2 + 56x^5y^3 + 70x^4y^4 + 56x^3y^5 + 28x^2y^6 + 8xy^7 + y^8

Well,

just build the triangle of Pascal according to the following construction rule :

1

1___1

1___2___1 ------------------> range 2

1___3___3___1

1___4___6___4___1

1___5__10__10___5___1

1___6__15__20__15___6___1

1___7__21__35__35__21___7___1

1___8__28__56__70__56__28___8___1 ---> range 8

and you have all coeeficients, that is the 8Ck for k = 0 to 8

8C0 = 1 , 8C1 = 8 , ..., 8C4 = 70 ...

(x + y)^8 = x^8+8x^7y+28x^6y^2+56x^5y^3+70x^4y^4 + ...

hope this helps !!