Question

Find the coefficient of $a^2{b}^3{c}^{4}d$ in the expansion of $(a-b-c+d{)}^{10}$.

Answer 1

The magnitude of coefficient of $a^2{b}^3{c}^{4}d$ in the expansion of $(a-b-c+d{)}^{10}=\frac{10!}{2!\times 3!\times 4!\times 1!}=12600$

For the sign we would see in the expansion we have $+a,-b-c,+d$ so we just raise it to the respective powers what would be$+a^2,-b^3,+c^4,+d$

All the terms are positive except $b$ is negative. Hence, the coefficient would be $-12600$