In this lesson, we're going to talk about multiplying using expanded form. You might want to watch the video on expanded form to refresh your memory. If you're ready, we're going to take an example problem and walk through it together. After that, you can try the other two problems on your own or work through them with me. The example problem is 45 multiplied by 12. In expanded form, 45 is 40 tens plus 5 ones, so it can be written as 40 + 5. 12 is one group of ten plus two ones, or 10 + 2. To multiply, we do some cross-multiplying from the top numbers to the bottom numbers. We multiply 40 by 10 and 40 by 2, then 5 by 10 and 5 by 2. The products are as follows: 40 times 10 is 440, 40 times 2 is 80, 5 times 10 is 50, and 5 times 2 is 10. To get the total sum, we add up the products. We line them up based on their place values. Zero plus 8 plus 5 is 13, plus one more is 14. One plus four is five. Therefore, the answer for 45 multiplied by 12 is 540. You can use lattice multiplication or standard multiplication to check your work. Now, let's move on to the next problem. We have 36 written in expanded form as 30 + 6, and 15 as 10 + 5. We follow the same strategy as before, multiplying both the top numbers with the bottom numbers. The products are: 30 times 10 is 300, 30 times 5 is 150, 6 times 10 is 60, and 6 times 5 is 30. After adding up the products, we get 540 as the answer. Lastly, we have 72 multiplied by 19. In expanded form,...