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
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.
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.