When introducing distributive property, I usually relate it back to how students would multiply a single digit and two digit number. So, for example, I'd ask what is 2(34), they'd reply 68, and when asked how they got it, they'd usually say something like 2x3 and 2x4, so I'd show how they were really doing 2(30+4)=60+8=68, and then move on to 2(3x+4).

One of my students though, wrote out the vertical multiplication and showed me that way. Thinking about it, I wondered if that might be a better way to demonstrate the property

2x + 4

3

-------

6x + 8

and then I thought, hang on, this would make multiplying two binomial expressions much cleaner

2x + 3

4x + 5

------------------

10x + 15

8x^2 + 12x

------------------

8x^2 + 22x + 15

and if, like me, you like to throw in multiplying multinomials so the don't get stuck in the prison of FOIL, this would make the gathering of like terms so much easier.