Interpret complex expressions by treating meaningful sub-expressions as single units.
Interpret an outside coefficient as the number of repeated groups
Problem
For \(5(x~+~2)\), \(\text{five}\) bags each contain \(x\) pencils and \(2\) pens. Interpret the outside coefficient, the groups it counts, and one group's contents.
Big Picture
What this problem is really about
An outside coefficient acts on the entire parenthesized group. We’ll first read the inside as the complete contents of one bag, then interpret the outside factor as the number of identical copies of that bag. Expanding to a repeated sum checks that every kind of item inside is reproduced for every group.
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