Video1: Multiply 2 Binomials using Distributive Poperty
High School / Math
Hi, class. This is miss champagne, and today I'm going to cheat you a one Z 8, which is called multiply two binomials. Which is a very fancy way to say that we're going to multiply X plus 6 times X plus 9. So let's first start out with labeling our sides. If this side is X plus 9, this side is X plus 9 as well, if this is X plus 6, this side is X plus 6. We're going to find our area and our perimeter. So to find the area, of course we know we multiply two numbers. So I'm going to put the hashtag for numbers. Only. So only two numbers. So I'm only going to multiply this side times this side. So we have X plus 9. And the parentheses means times. X plus 6. When you have two parentheses with no addition or subtraction in the middle, that means that you're going to use a method called foil, or you can divide these two and do the distributive property, whichever is easier for you. So first I'm just going to divide this and do the distributive property. So I'm going to put my X here, and then I'm going to put my X plus 6 here. I'm going to put my 9 here and my X plus 6 here. And then I'm going to add them to the other. In order to use the distributive property, you put your X twice, this X comes here. You have your plus sign in the middle. The 6 comes here. And you put your multiplication symbol at either end. Remember we learned when we multiply variables. There's two X's that two goes in the air. So let's bring down our plus sign. We have 6 times X, which is 6 X and we're going to add that to what we get over here. So we're going to distribute. We're going to put the 9 twice. Put a plus in the middle. My X comes here. About 6 comes here. With the multiplication symbols at either end, 9 times X is 9 X plus 9 times 6, 6 times 8 is 48. 49, 50, 51, 52, 53. 54, 55. 6 times 8 is 48. This is one, two, three, four, 5, 6, 7, 8, 9. So 48, 49, 50, 51, 52, 53, 54, 55, 56, 7. Now that's not right. 6 times 6. 36. Let me draw 6 lines one, two, three, four, 5 6, three, 6. So 7 39 four for one 42. So 6 times 7 is 42. For 3.4 for the purposes for ten 48, 6 times 8 is 48. 49 50, 51, 52, 53, 54, 6 times 9 is 54. Okay? So 9 times 6 or 6 times 9 is the same thing as 54th. And then we combine our like terms, so this has an X that's a positive 6 X and this is a positive 9 X we combine our two numbers in the middle, bring down our X squared plus 9 plus 6 is 15. Remember when we add variables, this number goes out front. And we leave our variable exactly the same. So 15 X plus 54. This is our area. Because we just multiplied the two binomials together. Now, when we find the perimeter, I'll go over here and put. Perimeter. That means we're going to add X plus 9 plus X plus 9. Plus, what it looks like time, let me raise it. I'm going to put plus X plus 6 plus another. X plus 6. And we're going to combine like terms. I have one, two, three, four X's. Remember when we're adding that number four, goes out front, the X goes behind it. So I'm going to square these out so I don't get confused. My exes are now added together. Then I'm going to add my numbers 9 plus 9 is 18. Plus 6 more, let me draw 6 lines so I can count. So that's 18, 19, 20, 21, 22, 23, 24, count 6 more. 25, 26, 27, 28, 29, 30. So four X plus 30. Is our perimeter. So we have four X plus 30 is the perimeter and the area is X squared plus 15 X plus 54.