find the 4th term of the expansion of (x-4y)^7

Question

raden · Answer

it is 7C3 x^(7-3)(-4y)^3
then simplify

kenljw · Answer

1                                  1
1 1                               2
1 2 1                            3
1 3 3 1                         4
1 4 6 4 1                      5
1 5 10 10 5 1               6
1 6 15 20 15 6 1          7
(x+(-4y))^7
forth term
20 x^(7-3) (-4y)^3 = -20X4^3 x^4 y^3
The triangle I derived is easy to develop it's called the Pascal Triangle and is used for coefficients of a binomial.

raden · Answer

7C3 = 7!/(7-3)!3! = 7!/4!3! = 7.6.5.4!/4!3! = 7 * 5 = 35

anonymous · Answer

then wat about (x-2y)^4, the 4th term in expansion?

kenljw · Answer

(x+(-2y))^4
there are four terms
(-2y)^4 = 16y^4

kenljw · Answer

sorry 5 terms
x(-2y)^3 = -8xy^3

raden · Answer

http://www.wolframalpha.com/input/?i=%28x-2y%29%5E4

kenljw · Answer

for 7 and need to add one more line to trangle
1 7 21 35 35 21 7 1
35 x^(7-3) (-2)y^3 = 35X(-2)^3x^4y^3