what is the definition of coeificents?

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

12

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 y^{2} with a coefficient.

3y^{2}, y^{2}, -y^{2}, 26y^{2}

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, 19y^{2}, 31y^{5}

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

19x, 14xy