Question:

If the coefficients of $x$ and $x^2$ in $(1+x)^p(1-x)^q$ are $4$ and $-5$ respectively, then $2p+3q$ is equal to

Step-by-Step Solution

Key Concept: Expand $(1+x)^p(1-x)^q$ to get: coeff of $x=p-q=4$ and coeff of $x^2=\frac{(p-q)^2-(p+q)}{2}=-5$.

$p=15,\ q=11$. $2p+3q=63$.

Correct Answer: 4