1. **State the problem:** Expand the expression $ (x-3)(x+5) $. 2. **Formula used:** Use the distributive property (also known as FOIL for binomials): $$ (a+b)(c+d) = ac + ad + bc + bd $$ 3. **Apply the formula:** $$ (x-3)(x+5) = x \cdot x + x \cdot 5 - 3 \cdot x - 3 \cdot 5 $$ 4. **Calculate each term:** $$ = x^2 + 5x - 3x - 15 $$ 5. **Combine like terms:** $$ 5x - 3x = \cancel{5x} + \cancel{-3x} + 2x $$ 6. **Final expanded form:** $$ x^2 + 2x - 15 $$ This is the expanded form of the given expression.