Evaluate : $123 \times 999 + 123$

### Concept & Formula This problem can be efficiently solved using the **Distributive Law of Multiplication** over addition: $$a \times b + a \times c = a \times (b + c)$$ ### Step-by-Step Solution * **Step 1:** Rewrite the expression to make the common factor explicit: $$123 \times 999 + 123 \times 1$$ * **Step 2:** Factor out the common term $123$: $$123 \times (999 + 1)$$ * **Step 3:** Simplify inside the parentheses and multiply: $$123 \times 1000 = 123000$$ ### Exam Strategy & Shortcut **Distributive Property:** Never multiply $123 \times 999$ directly. Recognize that $999$ is $1$ less than $1000$. Adding $123$ to $123 \times 999$ simply completes the group to make exactly $123 \times 1000$, which instantly gives $123000$. ### Common Pitfall * **Brute Force Multiplication:** Spending valuable time performing long multiplication for $123 \times 999$ increases the risk of calculation errors. Always look for algebraic simplifications when numbers like $99$, $999$, or $9999$ appear. ### Final Answer **Therefore, the correct answer is 123000.**