1. **State the problem:** Simplify the expression $ (x+3)(x-4) $. 2. **Formula used:** To multiply two binomials, use the distributive property (FOIL method): $$ (a+b)(c+d) = ac + ad + bc + bd $$ 3. **Apply the formula:** $$ (x+3)(x-4) = x \cdot x + x \cdot (-4) + 3 \cdot x + 3 \cdot (-4) $$ 4. **Calculate each term:** $$ = x^2 - 4x + 3x - 12 $$ 5. **Combine like terms:** $$ = x^2 - \cancel{4x} + \cancel{3x} - 12 = x^2 - x - 12 $$ 6. **Final answer:** $$ x^2 - x - 12 $$ This is the simplified form of the product of the two binomials.