 Do you wish there was a visual, fun way to perform binomial multiplication? Wait, what even is binomial multiplication? And how does it even work? Join me and discover the joy in math as we explore these questions in today's episode of Mr. Mark's Math Adventures. I'm Mark Lennifuss, but it's time to learn today. Time will tell you never say what to yourself, okay? My teacher, Mr. Mark, she got the funny math flow. Mr. Mark's math, the best of your time, let's go. Hey, math learners. It's Mr. Mark, your friendly neighborhood math teacher. Remember, it's not just about getting the right answers, it's about learning and growing along the way. Now, before we dive into today's adventure, remember to hit that subscribe button and ring the bell to stay tuned for future episodes. Now, if I got something special for you today, today, we're gonna be taking a sneak peek into the world of multiplying binomials, specifically using a little something called the box method. Now, don't worry if that does sound a bit scary. While I do encourage you to look deeper into these ideas, that's for another day. Today, we're just gonna have some fun trying to spot some connections. Now, what do you say we work through a problem together? As I work, keep a close eye on what I'm doing and see if you can spot some rules and patterns that I'm following. And as we begin, always feel free to use the companion worksheet with each episode. It's free to download, link down in the description. Now, here we have two polynomials, the polynomial two X plus three and the polynomial X plus five. Now, multiplying these two polynomials together might seem tricky at first, but let me show you one of my favorite visual methods. First, we draw a large box and divide it into four smaller boxes arranged in two rows and two columns like this. Next, we write the two terms of the polynomial two X plus three along the top and the two terms of the polynomial X plus five along the left side. It should look something like this. Now, we multiply the column value by the row value for each small box. Let's break it down box by box. In our first box, we multiply the term of the first column two X by the terms of the first row X. So two X times X gives us two X squared. Moving to the top right box, we multiply the term of the second column three by the term of the first row X. That's three times X giving us three X. Now, in the bottom left box, we multiply the term of the first column two X by the term of the second row five. This results in 10 X. And finally, in the bottom right box, we multiply the term of the second column three by the term of the second row five. That's three times five, which equals 15. And now that we filled all the boxes, we're gonna simply combine these four terms, simplify, and that's it. Two X squared, three X, 10 X, and 15, three X plus 10 X is 13 X. So our final simplified polynomial is two X squared plus 13 X plus 15. And there you have it. Just look at how each term interacts with the other. The box method organizes the problem and ensures we keep track of every term as we perform the multiplication. And now with your wheels turning, I have a challenge for you to try on your own. Can you use your observations of my actions to multiply the polynomials three X squared plus two X plus one and X squared plus X minus four. Using the box method, share your answers and reasonings in the comments below. Remember, it's not just about figuring it out the first time, but about giving it a shot and trying your best. Hey, and here's a hint. Notice how each polynomial now has three terms instead of two. How does that alter our initial box method setup? Do you think? Props to you for taking some time out of your day to do some math with me. I hope you followed along, and if you made mistakes, that's all good. Remember that every mistake is a step towards learning something new. And hey, Mr. Mark's math adventures is holding a giveaway. Click the link in the description below to see the giveaway details and for your chance to win. This is Mr. Mark signing off. I'll catch you next time with another math problem. What did you think? Did you approach this problem differently? Let me know in the comments. And if you enjoyed this problem, show your support by liking and sharing this video. And don't forget to follow my page to stay up to date on more math related content. Until next time.