Question

How is multiplication using products different from multiplication using regrouping? How are they the similar

Answer 1

Partial products are different in regrouping in terms of how numbers are clustered from a set equation as a whole delivering it individual but naturally to all the numbers involved in the set. 
Regrouping is just like the commutative or associative property of numbers.
Associative property of addition is used when you want to group addends. This is mainly used to cluster set of numbers or in this case, addends. How do you use the associative property when you break apart addends? Simple you group them using the open and closed parentheses or brackets. Take for an example 1 + 1 + 2 = 4. Using the associative property you can have either (1 + 1) + 2 = 4 or 1 + (1 + 2) = 4 clustered into place.