Distributive theory EASY. Especially if you've been doing it since you were four. But even if you haven't base ten blocks make it easy to understand. This is an explanation the THE explanation. Makes the idea easy to see, the symbols become visually obvious and we take the concept from the abstract to the concrete with base ten blocks.
When working with young children the algebra is just along for the ride, we are much more interested in addends and multiplication.
You could use the blocks to show 3(2 + 7), use three's and you'd have two rectangles one with 6 and the other with 21, one above the other...three across and then 2 up and then 7 more up...
The Algebra is just as easy to get. Using the blocks and building bigger, funner problems makes it simple child's play.
More explanation can be done by flipping the blocks over and showing (10 + 3)(10 + 2), now instead of x squared and x's and units we have a hundred tens and units. Same blocks we could do percentages too. Imagination is powerful and these tools help unlock it and put it to use...also helps with visualization.
The distributive property is easy with base ten blocks and so it the associative property. That page BTW is far and away the most popular webpage I've ever built getting thousands of hits per month, month after month year after year. Why? Because base ten blocks make math concepts easy to understand.