Problem: Compute \( 117 \cdot 1001 + 9 \cdot 999 \cdot 13 \).
If you got an answer, congratulations!
Did you multiply the products out?
If you did, and it took a long time, no worries! Read on, because this question has a really cool solution you won’t want to miss.
Let’s think through this together. When we start a problem, we usually think about what things are given and how the problem is stated. What do you see here?
There’s a sum of two products… and the numbers look quite big and ugly. We can certainly multiply each product out (do \( 117 \times 1001 \) and \( 9 \cdot 999 \cdot 13 \) before adding them), but if we do so, we could make a silly mistake in our multiplication.
Unless you’re a multiplication master, this is probably not the most efficient way. In fact, your teachers in school may not be able to see how to do this problem in quicker than multiplying the numbers out and adding them.
What to do now? Is there a faster approach? Think about this before you move on.