simplify the expression 3a+4b-3a-b

Question

i am not clear about combining like terms can you please help me understand?

Answer 1

Devora,

When you see problems like you posted 3a+4b-3a-b, sometimes it is easier to see them separately.

For example: 3a+4b-3a-b

Can be viewed as:

3a

4b

-3a

-b

and since there is no multiplication or division involved you can perform this in any order you want.  So you could rewrite the equation like this: 3a-3a+4b-b.  

3a-3a is 0 so now we can rewrite the equation like this: 4b-b.  Then we just finish simplifying 4b-b= 3b.

I hope this helps, if yo have any questions let me know.

Answer 2

The way to do this sort of problem is to combine the values with common variables. In this case "a" and "b" are the variables and the values in front of each of these variables are their coefficients.

for example:

3a is actually the value 3 times the variable a

4b is the value 4 times the variable b

To do this problem you will "group the like terms" using their operations.

3a + 4b - 3a -b

Step 1: group 3a and -3a together

3a - 3a = 0

Since the a variable is common in both of these terms you are able to group them together. Now we notice that each of these has a 3 in front of them. This allows you to perform the operation by which they are stated in the problem. So in essence, 3a - 3a is equal to 0 in this case, so in this problem the "a" variable would disappear in the solution.

Step 2: Group 4b - b

4b is equal to 4 times b and -b is equal to (-1) times b

so performing this subtraction the result would be 3b.

Step 3: The total solution from Steps 1 and 2 will result in your final answer of 3b.

3a - 3a + 4b - b

equals 0 + 3b = 3b as your final answer

 

I hope this helps

Answer 3

Hi Devora,

I would like to explain combining like terms to you.

The expression 3a+4b-3a-b has four terms: 3a,  4b,  -3a,  and -b.

Like terms are the one s with common variable parts: 3a and -3a are like terms, 

4b and -b are also like terms.

To combine 3a+(-3a) we'll use distributive property: ab+ac=a×(b+c).

a is common factor, it goes outside the parenthesis: 3a+(-3a)=a×(3+(-3))=a×0=0.

b is a common factor for 4b+(-b)=4b+(-1b)=b×(4+(-1))=b×3=3b

The answer is 0+3b=3b.

As you can see, when you use distributive property to combine like terms, you end up adding coefficients of those terms.

Hope it helps.