1. **State the problem:** We are given the function $f(x) = 5(x-8)(x+2)$ and asked to analyze or simplify it. 2. **Formula and rules:** This is a quadratic function in factored form. To simplify or expand, use the distributive property (FOIL method) for binomials: $ (a-b)(c+d) = ac + ad - bc - bd $. 3. **Expand the factors:** $$ (x-8)(x+2) = x \cdot x + x \cdot 2 - 8 \cdot x - 8 \cdot 2 = x^2 + 2x - 8x - 16 $$ 4. **Simplify the middle terms:** $$ x^2 + 2x - 8x - 16 = x^2 - 6x - 16 $$ 5. **Multiply by 5:** $$ f(x) = 5(x^2 - 6x - 16) = 5x^2 - 30x - 80 $$ 6. **Final answer:** $$ f(x) = 5x^2 - 30x - 80 $$ This is the expanded form of the given function, which is easier to analyze for graphing or finding roots.