 How to add or subtract polynomials? What do you get when you add two cats and three dogs? Let me think five cat dogs No, right? Because the cats continue to be cats and the dogs continue to be dogs I mean you may have five pets, but you still have two cats and three dogs Now we can apply this same principle when we add polynomials Because what property do we use when we add things? Yes, we add things with the same name Consider this if Julia has three cats and one dog and Jeremy has one cat and two dogs What can you say about their combined number of cat and dogs? Well, let's use C for cats and D for dogs So Julia Julia has three cats. Let's say three C and one door That's right one D and We want to combine them so combined means we have to add them We're going to add the number of pets that Julia has with the dogs and cats that Jeremy has This heat Jeremy has one cat. So we'll see one C and Two dogs plus two D. Now when we add this we know that They have four cats four C and that they have three dogs all together We are adding things with the same name cats with cats sees with sees and dogs with dogs These with these now, of course, we didn't need to write this one here or here But we wrote it just for a clarification Now let's look at subtraction What if Two cats and one dog from their combined number of pets die What could we say about their combined number of cats and dogs? You have four cats all together Julia and Jeremy. Hey, they have four cats and they have three dogs Mmm, and we want to subtract those that will die so One two cats will die and one dog will die Now we know that if we had four cats and two die We're gonna and we're gonna end up with two cats and then if we had three dogs and one dies We're going to end up with two dogs But notice that in order for this to happen You know, we're subtracting this guy from C and this guy from D So this is just for C Plus 3d Minus 2c Minus right we're distributing that minus sign minus D and now we combine like terms for C minus 2c plus 3d minus D is equal to 2c plus 2d, which is exactly this