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(m+n)p=p(m+n) illustrates what property?

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(m+n)p=p(m+n) illustrates the "Commutative Property". When two numbers are multiplied together (m+n) and (p), the product is the same regardless of the order of the multiplicands [whether (m+n) comes first or (p) comes first].

Associative, because it doesn't matter which comes first.  If we let (m+n) = x, then we'd have x*p = p*x, where the order obviously doesn't matter.

After you multiply p times m+n, we have mp + np = pm + pn, which is called Distributive, because we are "distributing" the letter p across both m and n