What does combining like terms look like

Question

I need to know this for homework tonight

Answer 1

Combining like terms means that when we have variables that are of the same value, we can add them together.

 

For example 2w + 4w. since they both have the same variable used, we can add them together to make 6w (since 2+4=6).

 

Let me show you a couple concrete examples:

let's say our w variable is 2. That would mean the equation would look like:

2*2 + 4*2 = 6*2

4 + 8 = 12

12 = 12

 

And again with w = 3:

2*3 + 4*3 = 6*3

6 + 12 = 18

18 = 18

 

And it works exactly the same sort of way no matter what we plug in for our w.

 

So as long as the variable remains the same, we can add or subtract them:

 

40w -10w = 30w

5w + 10w -3w → 15w - 3w = 12w

 

Remember, that's if they are like variables. If we add in another variable, we cannot add them together:

3x + 4y = 3x + 4y

The variables will most likely have different values, so we cannot combine them together to make 7xy. Remember, when the variables are next to each other and the integers, we are multiplying instead of adding.

 

Example. Let's say x = 3 and y = 8

3*3 + 4*8 → 9 + 34 = 43

7*3*8 = 168

43 =/= 168

 

But if we have a few different variables that have similar values, we can combine them in that case:

3w + 6y + 2w + 7y

We can combine the w variables together and get 5w. Similarly, we can combine the y variables to get 13y, so our final equation looks like:

5w + 13y

 

I hope this gives you some insight into how combining like terms works.

Answer 2

Hi Alain--

 

"Combining terms" means to group together any terms in an equation or expression that can be combined. For example, in the expression 4a + 2 - 3a + 5, you can combine the "a" terms of 4a - 3a to get 1a (which you would call simply "a"), and the numerical terms 2 + 5 to get 7.

 

So combining the terms in that expression would result in a much "cleaner" expression, a + 7.

 

Hopefully that will get you started.

 

Matt in New York