Use the distributive property to expand and factor simple linear expressions.
Check which forms are equivalent
Problem
Apply distribution and repeated-addition reasoning to \(3(x~+~2)\). Test \(\text{every}~\text{labeled}~\text{expression}\) below for equivalence, then report the \(\text{complete}~\text{set}~\text{of}~\text{valid}~\text{labels}\).
A. \(3x~+~6\) B. \(x~+~6\) C. \(6~+~3x\) D. \(3(x~+~6)\) E. \(x~+~2~+~x~+~2~+~x~+~2\)
Big Picture
What this problem is really about
Create one dependable comparison form by distributing the three across the original group. Then test every labeled expression against the entire structure, remembering that reordering addends does not change a sum and repeated addition can represent multiplication. A form fails if it changes the number of variable copies or the constant contribution.
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