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what does combine coeificents mean ?

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Lala, what your are talking about here is the concept of "Combining Like Terms" and it is a key piece of the puzzle when solving algebric equations.  

Combining Like Terms is a process used to simplify an expression or an equation using addition and subtraction of the coefficients of terms. Consider the expression below:

5 + 7

By adding 5 and 7, you can easily find that the expression is equivalent to


Algebraic expressions can be simplified like the example above by Combining Like Terms. Consider the algebraic expression below:

12x + 7 + 5x

12x and 5x are like terms because they both contain the variable "x". Therefore the coefficients, 12 and 5, can be added. This is a simple example of Combining Like Terms.

17x + 7

Another way to think about it is you are "factoring" out (a term you will here a lot in algebra class and beyond" the "x" term

x (12 + 5) + 7

What are Like Terms?

The key to using and understanding the method of Combining Like Terms is to understand like terms and be able to identify when a pair of terms is a pair of like terms. Some examples of like terms are presented below.

The following are like terms because each term consists of a single variable, x, and a numeric coefficient.

2x, 45x, x, 0x, -26x, -x

Each of the following are like terms because they are all constants.

15, -2, 27, 9043, 0.6

Each of the following are like terms because they are all y2 with a coefficient.

3y2, y2, -y2, 26y2

For comparison, below are a few examples of unlike terms.

The following two terms both have a single variable with an exponent of 1, but the terms are not alike since different variables are used.

17x, 17z

Each y variable in the terms below has a different exponent, therefore these are unlike terms.

15y, 19y2, 31y5

Although both terms below have an x variable, only one term has the y variable, thus these are not like terms either.

19x, 14xy