Combining like terms
Sal explains why 4a + 2a = 6a several ways. Created by Sal Khan.
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- i don't under stand at1:20Please help :((9 votes)
- Are you asking about how Sal said that the variable a can represent anything? What Sal meant was that if their is a question like 7b + 4b the variable b would not have to represent a specific object that begins with b. A certain amount of boxes could be the variable n. Also in a problem (lets say 6c + 2c) if the same variable is used that means its the same object. 6c & 2c both represent the same object. Hope this helped!(10 votes)
- ok so what happens if a question like this occurs : 3a + 9b = ?
Would it be 12ab?(5 votes)
- Unless they ask you to do a specific formula like substitution or elimination, that should be right.(8 votes)
- We are studying problems that say name the like terms, -x to the 4th the power, 2x to the 3rd power, -5x the 4th power, -8x to the 2nd power, -6x to the 2nd power, -7x the third power and we are given options to choose from. I don't understand what they are asking. Am I supposed to combine like terms?(9 votes)
When typing exponents, you can use the symbol "^" to mean "raised to the power of" So your equation can be written as
-x^4 + 2x^3 - 5x^4 - 8x^2 - 6x^2 -7x^3
To combine like terms, you want to first reorder the terms so the powers are from highest to lowest.
-x^4 - 5x^4 -7x^3 + 2x^3 - 8x^2 - 6x^2
The like terms can be combined. That is, the terms with the same power can be combined. I'll write it with parenthesis first to show which ones can be combined.
(-1x^4 - 5x^4) + (-7x^3 + 2x^3) + (- 8x^2 - 6x^2)
which when the like terms are combined becomes
- 6x^4 - 5x^3 - 14x^2
I hope that helps answer your question.(5 votes)
- So 100 + 100 + 100c + 100c = 200 + 200c?(7 votes)
- what about when the second number is just a variable like
- Well, when any variable is by itself, imagine a one in front of it, because it is 1a. 4a = 4a and 1a = 1*a = a
The answer to 4a+a = 5a
Hope this helped!(4 votes)
- i didn't get points for this! and my teacher gave this "combining like terms to me and my friends what is wrong?(5 votes)
- combing like terms is adding a variables to the same letters(4 votes)
- Why do you do it this way? Basically if you think of 3x + 4x, you add the coefficients to get 7x. The idea behind this strategy is:
3x = x + x + x
4x = x + x + x
Think of x as the number of x-rays printed. Now, count the total number of x-rays: x + x + x + x + x + x + x
That's right! 7x.
Now think of 4f + 4g. f is fruit and g is grain. Grain and fruit are different, and no values are provided so it is not possible to make such conclusions in this expression.
HOPE DOUBTS CLEAR! 🤗(6 votes)
- how could I answer something like -6(3+4x) Id really love a response quick since I have a test and I'm barely prepared! D:(6 votes)
- what happens if you got a question like this 5b+9p= what?(4 votes)
- In that case, those terms cannot be combined because they are not like terms, and you now have what is called a multivariable equation.(5 votes)
- no way there is a comment section here(4 votes)
Let's say that you started off with 3 apples. And then I were to give you another 7, another 7 apples. So my question to you-- and this might be very obvious-- is how many apples do you now have? And I'll give you a second to think about that. Well, this is fairly basic. You had 3 apples. Now, I'm going to give you 7 more. You now have 3 plus 7. You now have 10 apples. But let's say I want to do the same type of thinking, but I'm too lazy to write the word "apples." Let's say instead of writing the word "apples," I just use the letter a. And let's say this is, say, a different scenario. You start off with 4 apples. And to that, I add another 2 apples. How many apples do you now have? Instead of writing apples, I'm just going to write a's here. So how many of these a's do you now have? And once again, I'll give you a few seconds to think about that. This also might be a little bit of common sense for you. If you had 4 of these apples or whatever these a's represented, if you had 4 of them and then you add 2 more of them, you're now going to have 6 of these apples. But once again, we started off assuming that a's represent apples. But they could have represented anything. If you have 4 of whatever a represents, and then you have another 2 of whatever a represents, you'll now have 6 of whatever a represents. Or if you just think of it if I have 4 a's, and then I add another 2 a's, I'm going to have 6 a's. You can literally think of 4 a's as a plus a plus a plus a. And if to that, I add another 2 a's-- so plus a plus a, that's 2 a's right over there-- how many a's do I now have? Well, that's 1, 2, 3, 4, 5, 6. I now have 6 a's. So thinking of it that way, let's get a little bit more abstract. Let's say that I have 5 x's, whatever x represents. x could be some number. So I have 5 of whatever that number is. And from that, I subtract 2 of whatever that number is. What would this evaluate to? How many of these x's would I now have? So it's essentially 5x minus 2x is going to be what times x? Once again, I'll give you a few seconds to think about it. Well, if I have 5 of something and I subtract 2 of those away, I'm going to have 3 of that something left. So this is going to be equal to 3x. 5x minus 2x is equal to 3x. And if you really think about what that means, five x's are just x plus x plus x plus x plus x. And then we're going to take away two of those x's. So take away one x, take away two x's. You are going to be left with three x's.