If in the expansion of $(1 + z)^m(1 - z)^n$ the coefficients of $z$ and $z^2$ are $-6$ and $-6$ respectively, then the value of $m + n$ is
Step-by-Step Solution
Key Concept: Coefficient matching in binomial expansions with negative indices requires careful algebraic manipulation of the general term.
Expanding $(1+x)^m(1+x)^n$ using the binomial theorem and comparing coefficients, we find that $m = n = -2$ and the relationship $mn = -6$ must hold. Given the constraint that $m - n = -2$ and $mn = -6$, solving these simultaneous equations yields $m = 7$ and $n = 9$.
Correct Answer: 7