Use commutative, associative, and distributive structure to rewrite and simplify numerical expressions efficiently.
Check rewrite validity and use a specified target structure
Problem
For \(18~\times~5\), Rewrite A is \((10~\times~5)~+~(8~\times~5)\), and Rewrite B is \(18~\times~(5~+~5)\). Identify all valid rewrites. Use Rewrite A to find the product.
A rewrite is valid only if it preserves the original product. We’ll check whether each proposed form follows a true factor split, reject any form that changes a factor’s value, and evaluate the valid distributed split using its friendly partial products. That separates structural equivalence from mere reuse of the same numbers.
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