jmc

When using the distributive property for the first time, we add the product of $x+3$ and $x$ to the product of $x+3$ and $-8$:

$$\begin{array}{rl}(x+3)(x-8)& =(x+5)\cdot x+(x+5)\cdot (-8)\\ & =x(x+3)-8(x+3)\end{array}$$We use the distributive property again and combine like terms:

$$\begin{array}{rl}x(x+3)-8(x+3)& =x^2+3x-8x-24\\ & =\boxed{x^2-5x-24}\end{array}$$