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comgining like terms. what do these mean,11b -6 6v 5a 5c 6 -5b 2b what do or how do i use them..

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2 Answers

This may seem mysterious, because you have letters and numbers, but no one has told you what the letters stand for. 5a is easy if we know that a=2. 5a would equal 5x2 = 10 (another way to write that is 5*2=10)

In your question, you have many letters that are variables. a, b, c and v are your variables. The good news is that we don't have to know what numbers they represent in order to combine like terms. Combining like terms is another way of organizing the numbers. To use a picture, we can put all the apples with the other apples, bananas with the other bananas, and pizzas with the other pizzas. 

We started with    11b -6 6v 5a 5c 6 -5b 2b

Let's organize:

  • all the numbers with a ---    5a
  • all the numbers with b ---    11b, -5b, 2b
  • all the numbers with c ---    5c
  • all the numbers with v ---     6v
  • all the numbers with no variable --- 6, -6

Now that we have organized, we know what we can combine. There is no way for us to combine v+b.  That's ok. The numbers with a, c, and v have no like terms. Nothing matches them. 

We can combine the numbers with b. 11b - 5b +2b = 8b

We can combine the numbers with no variable 6-6=0

We are left with 5a, 8b, 5c, 6v

Like terms have the same variables with the same exponents.

From your list, 11b, -5b, and 2b are like terms because they all have the variable b (raised to the first power).

Also, -6 and 6 are like terms because they have no variables.

From the list that you gave, 6v, 5a, and 5c have no like terms, since each of them is the only terms with the given variable.

Like terms can be added and subtracted.  If terms are not like, then they cannot be added and subtracted.

(11b - 5b + 2b = 8b, 6 -6 = 0)