How do you find the coefficient of #a# of the term #ax^8y^2# in the expansion of the binomial #(x-2y)^10#?

1 Answer
Noah G
Feb 16, 2017

#a = 180#.

Explanation:

If we include the 0th term, then there will be 11 terms in this expansion. This means that the term #ax^8y^2# will be the third term (since #11- 8 = 3)#.

The formula for the nth term in a binomial expansion #(a+ b)^n# is given by

#t_(k + 1) = color(white)(two)_nC_ka^(n - k)b^k#

We have

#k + 1 = 3#

#k = 2#

Use the formula now.

#t_3 = color(white)(two)_10C_2x^(10 -2)(-2y)^2#

The value of #color(white)(two)_10C_2# can be computed using the formula #color(white)(two)_nC_r = (n!)/((n - r)!r!)#. Therefore, #color(white)(two)_10C_2 = (10!)/(8!2!) = 45#

#t_3 = 45x^8 4y^2#

#t_3 = 180x^8y^2#

Therefore, #a= 180#.

Hopefully this helps!

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