SOLUTION: 2. Expand:
a) (y−3z)^5
b) (2s−t^4 )^4
I know she wants us to use paschals rule but I'm not sure how to do it without making the whole triangle can you explain ho
Algebra ->
Permutations
-> SOLUTION: 2. Expand:
a) (y−3z)^5
b) (2s−t^4 )^4
I know she wants us to use paschals rule but I'm not sure how to do it without making the whole triangle can you explain ho
Log On
Question 1116458: 2. Expand:
a) (y−3z)^5
b) (2s−t^4 )^4
I know she wants us to use paschals rule but I'm not sure how to do it without making the whole triangle can you explain how to find coefficients without making the triangle Answer by greenestamps(13200) (Show Source):
I'll get you started by explaining how to get a few terms of the first example; then you can continue the process to finish that one and do the second one.
Think of this as 5 factors of (y-3z) multiplied together. The final expanded form consists of all the "partial products" formed by choosing one of the two terms from each of the 5 factors. For example, one partial product, obtained by choosing the "y" term from the first 2 of the 5 factors and the "-3z" term from the last 3 factors, is .
I will show you how to get the first three terms in the expansion of this first example....
(1) If you choose the "y" term from all 5 of the factors, the partial product is . And there is only one way to choose the "y" term from all 5 of the factors; so the first term in the expansion is .
(2) If you choose the "y" term from 4 of the 5 factors and the "-3y" term from the other, then the partial product is . The number of different ways of choosing the "y" term in 4 of the 5 factors is "5 choose 4", or . So the second complete term in the expansion is .
(3) Without all the explanation, the next complete term in the expansion will be .
