Coefficient of $$x^r$$ in a Product

Coefficient of $$x^r$$ in a Product

## Formula

If:

$$P(x)=\sum_{k=0}^{m}a_kx^k$$

and:

$$Q(x)=\sum_{k=0}^{n}b_kx^k$$

then the coefficient of $x^r$ in $P(x)Q(x)$ is:

$$\sum_{k=0}^{r}a_kb_{r-k}$$

## Usage

- Used to determine a particular coefficient when two polynomial expansions are multiplied.