Answer:
-1,959,552
Explanation:
You want to know the coefficient of x^5y^5 in the expansion of (2x -3y)^10.
Binomial expansion
The k-th term of the binomial expansion of (a +b)^n, with k ∈ [0, n], is ...
C(n, k)·(a^(n-k))(b^k)
Application
For n=10, k=5, the term is ...
C(10, 5)·(2x)^5(-3y)^5 = 252·32·(-243)·x^5·y^5
= -1959552x^5y^5
The coefficient is -1,959,552.
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Additional comment
The function C(n, k) tells the number of ways k elements can be chosen from a set of n, without regard to order. The value is ...
C(n, k) = n!/(k!(n-k)!)
Many graphing and statistical calculators can compute the value for you. In this case, it is ...
(10·9·8·7·6)/(5·4·3·2·1) = 3·2·7·6 = 252