Multiplying Functions

Multiplying functions multiplies their outputs. For $p\left(x\right) = x+4$ and $q\left(x\right) = x-1$, using both rules turns $p\left(x\right)\cdot q\left(x\right)$ into $\left(x+4\right)\left(x-1\right)$. Each rule gets its own brackets, because the whole output of p multiplies the whole output of q.

Then multiply out as in Algebra: every term of the first bracket times every term of the second. That gives ${x}^{2}-x+4x-4$, and collecting leaves ${x}^{2}+3x-4$.

Without the brackets, $x+4x-1$ would multiply only the 4 by x, which is a different function. Check with x = 2: p(2) is 6 and q(2) is 1, so the product is 6, and $4+6-4$ is 6 as well.