Problem: Compute \( 117 \cdot 1001 + 9 \cdot 999 \cdot 13 \).

We have a sum of products. In those situations, we usually multiply two numbers at a time. And if you recall our material we covered in Week 1, you may remember something called…

the distributive property.

Why should we think about that?

We have a sum of products, and applying the distributive property in reverse, if there is a common number being multiplied, we can “factor” out that number from the entire expression, as follows (for numbers \( a,b,c \) ) :

\( ab+ac=a(b+c) \)

And maybe, just maybe the sum \( b+c \) will be something nice to multiply by!

Can we apply it? If so, how?

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