Find the term of the binomial expansion containing y^13 of (x^2+y)^22
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To find the term of the binomial expansion containing y^13 of (x^2 + y)^22, we need to use the binomial theorem.
The general term of the binomial expansion is given by:
T(r+1) = (nCr)*(a)^(n-r)*(b)^r
In our case, a = x^2, b = y, n = 22, r = 13.
Plugging in the values, the term containing y^13 is:
T(14) = (22C13)*(x^2)^(22-13)*(y)^13
Calculating the coefficients and powers:
T(14) = (22!)/(13!*(22-13)!)*(x^2)^9*(y)^13
= (22!)/(13!*9!)*x^18*y^13
Simplifying further:
T(14) = (22*21*20*19*18*17*16*15*14*13!)/(13!*9*8*7*6*5*4*3*2*1)*x^18*y^13
= (22*21*20*19*18*17*16*15*14)/(9*8*7*6*5*4*3*2)*x^18*y^13
The term of the binomial expansion containing y^13 is:
(22*21*20*19*18*17*16*15*14)/(9*8*7*6*5*4*3*2)*x^18*y^13
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