What do I have? Or another way to say it, And now it should beĪ little bit simpler. Reordered the statement and I've color coded it based Have one y squared term- I'll circle that in And then let's see, I haveĪn x term right over here, and that actually looks Do I have any other x squared? Yes, I do. Now, let's thinkĪbout- and I'm just going in an arbitrary order,īut since our next term is an xy term- let's think aboutĮxpression- plus 4xy. See if there is anything that we can simplify. Than a y squared, is different than an xy. Guess you cannot add these two or subtract these two terms. The same letter here, they aren't the same- I Took on the value 3, then the y squared would If y was 3 and an x was aĢ, then a y would be a 3 while an xy would have been a 6. And there will be a temptation,ģy plus this 4xy somehow since I see a y and a y. Xy's, and x squared and x's, well more just xy's and Don't let setbacks like these decrease your confidence and motivation. Best of luck on your learning adventures, and remember that unlike y= mx +b, progress isn't linear. Once again, I hope my explanation was thorough enough, but feel free to reach out if it wasn't. There we have it! We successfully combined like terms with negative coefficients. I wouldn't worry too much about this, but rearranging it this way will help you in the future. I have had teachers that were picky about having the terms being ordered in descending order, from largest exponent to smallest, so I would rearrange it like This will give us -4x^2 (remember that the ^2 is a part of our variable, and because of that it will not change after we combine our coefficients), leaving us with Our 4x is the only term with an x variable, so we leave that alone. So, we can visualize the combination of these terms like 3+1. Remember that there is an imaginary 1 in front of the xy. Which added to the rest of the expression would be Continuing on, combining those terms gets us It is important to have a good foundation. I would just go back and review negative numbers before coming back to this topic. If you are unsure how to do this, that's okay! Don't worry. Starting with the y variables, we have 2y - 7y. For example, the z in 3z + 9z will stay z, even after we combine the coefficients to get 12. ![]() No matter what numbers we combine, our variable will always stay the same. Remember that when we combine terms to think of it like combining the coefficients. ![]() With that out of the way, our example becomes It helps to think of the + or - sign (and only + or - signs) in front of a term as being a part of the term itself. For example, if we wanted to rearrange x - 3xy, we would write it as -3xy + x because subtracting a term is the same as that term being negative. When doing this, remember the sign that the term carries. Knowing what was just covered, let's rearrange the terms so that all terms with identical variables are next to each other. In short, the variables following the coefficients need to be identical in order to combine them. In addition to multiplying by x, you are also multiplying by y. Even though both terms share an x, an xy is not the same as an x. That means we could combine an x with a 3x, because x is the variable in both of those terms, but we cannot combine a 4x with a 2xy. We can only combine terms that have the same variable. Before we do anything to combine these terms, we need to remember the rules for what terms to combine. ![]() So, as an example, 3x, 7y, 9z^2, and 4f are all terms. Remember that a term is any coefficient and any variable. If I don't cover what you are confused on, though, just tell me and I can explain that. ![]() I'm unsure what exactly you are confused about, so I will try to explain the entire concept as thoroughly as possible.
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