How do you use pascals triangle to expand #(2x-y)^3#?
1 Answer
Jan 10, 2016
Explanation:
In general, for
Note that, for example, C(4,0)=C(4,4)=1,C(4,1)=C(4,3)=4,C(4,2)=6
and Pascal's triangle gives a diagram representing binomial coefficients, namely:
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
etc.
The sequence of numbers in the i-th row are, respectively, C(1,0),C(i,1),C(i,2),C(i,3), etc.
The number C(i,j) is the sum of the two numbers C(i−1,j−1) and C(i−1,j) just above it in the diagram and to the left and right, respectively.
In this example,