jmc

First, we use the distributive property to expand the first two factors:

$$\begin{array}{rl}4(x-5)(x+8)& =(4\cdot x-4\cdot 5)(x+8)\\ & =(4x-20)(x+8)\end{array}$$We use the distributive property again by adding the product of $4x-20$ and $x$ to the product of $4x-20$ and 8:

$$\begin{array}{rl}(4x-20)(x+8)& =(4x-20)\cdot x+(4x-20)\cdot 8\\ & =x(4x-20)+8(4x-20)\end{array}$$ We use the distributive property again and combine like terms:

$$\begin{array}{rl}x(4x-20)+8(4x-20)& =4x^2-20x+32x-160\\ & =\boxed{4x^2+12x-160}\end{array}$$