SOLUTION: Use the binomial formula to find the coefficient of the z^14y^2 term in the expansion of (z-3y)^16

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Question 770274: Use the binomial formula to find the coefficient of the z^14y^2 term in the expansion of (z-3y)^16
Answer by nerdybill(7384) About Me  (Show Source):
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Use the binomial formula to find the coefficient of the z^14y^2 term in the expansion of (z-3y)^16
.
the formula is:
nCk
read: "n Combination k"
.
If you have z^14y^2
then
n is 16
k is 2
.
C
n k
.
n!/(n-k)!k!
16!/(16-2)!2!
16!/14!2!
(15*16)/(2)
15*8
120
.
now we have:
120z^14y^2
From: (z-3y)^16
substitute in our z and y
120z^14y^2
120z^14(-3y)^2
120z^14(9y^2)
1080z^14y^2 (answer)