 Now there's many variations on a theme of multiplication by using the distributive property, and so here's one example. We might use what's called distributive subtraction, because a distributive property also applies when we are subtracting. So if I have a times the product b minus c, I get the product a times b minus the product a times c. And this gives us the flexibility to find another way of multiplying two numbers. So for example, let's consider the product 85 times 19. This time we'll take advantage of the fact that 19 is 20 minus 1. And the advantage to that is that if I know that I'm going to be working with these numbers, it's much easier to work with a 1 and a 2 than it is with a 1 and a 9. So let's go ahead and expand that out. 85 times 19 is the same as 85 times 20 minus 1. And I can apply my distributive property 85 times 20 minus 85 times 1. Again, easy multiplication to do here, 1700 minus 85, and well, this is minus 85, so I'll subtract too much, so I'll go down to 1600, add back 15, and there's my product. Here's another example. Let's take the product 97 times 28, and in this case it might be worth noting that both of these are pretty close to an easy number to work with. So I might do this as 28 is 30 minus 2. So 97 times 28, 97 times 30 minus 2, and that expands 97 times 30, 97 times 2. Somewhat more difficult to do this multiplication here, 97 times 30, and that works out to be 2910, 194, and do the subtraction, and we end up with this as our answer. Again, one possibility, subtract 200, return 6. On the other hand, we might use the fact that 97 is pretty close to 100. So I'll use 97 as 100 minus 3, and I'll apply commutativity. So 97 times 28 is the same as 28 times 97, and that's 28 times 100 minus 3, and again 28 times 100, really easy multiplication there, 28 times 3, well, let's use the distributive property to think our way through this. Plus 28 times 3, so that's 60, plus 24, so that's 84, and again, product 2800 minus 84 gives us 2716.