Question

Your friend used the distributive property and got an expression 4x +12y - 32. What algebraic expression could your friend have started with?

Answer 1

The "inverse" operation of the distributibe property is factoring common terms: since the litera part is different for each term (we have a term involving x alone, a term involving y alone, and a pure number), we can only factor the numerical part.

4, 12 and 32 have factor 2 or 4 in common, so the two possible algebraic expression could be

$2(2x+6y-16)$

$4(x+3y-8)$