1. **State the problem:** Simplify the product using the Distributive Property: $$(a - 3)(a - 4)$$ 2. **Recall the formula:** The distributive property for two binomials is: $$ (x + y)(z + w) = xz + xw + yz + yw $$ 3. **Apply the distributive property:** $$ (a - 3)(a - 4) = a \cdot a + a \cdot (-4) + (-3) \cdot a + (-3) \cdot (-4) $$ 4. **Calculate each term:** $$ a \cdot a = a^2 $$ $$ a \cdot (-4) = -4a $$ $$ (-3) \cdot a = -3a $$ $$ (-3) \cdot (-4) = 12 $$ 5. **Combine all terms:** $$ a^2 - 4a - 3a + 12 $$ 6. **Simplify like terms:** $$ a^2 - \cancel{4a} - \cancel{3a} + 12 = a^2 - 7a + 12 $$ **Final answer:** $$ (a - 3)(a - 4) = a^2 - 7a + 12 $$