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For positive integers m and n, suppose (1 - y)^m(1 + y)ⁿ expands as 1 + a1 y + a2 y² +.... If a1 = a2 = 10, then the ordered pair (m, n) is

1. (20,45)
2. (35,20)
3. (45,35)
4. (35,45)

Correct answer: (35,45)

Solution

For (1-y)^m(1+y)^n, a1=n-m=10. The x^2 coefficient gives (n-m)^2-(m+n)=2*a2 -> 100-(m+n)=20, so m+n=80. Solving with n-m=10 gives n=45, m=35, i.e. (m,n)=(35,45).

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