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?