Sometimes, some algebraic expressions need to be simplified by adding (or subtracting) terms that have the same variable.
We encounter the necessity of simplifying these expressions when we develop an algebraic expression or solve an equation or an inequality. But it is also necessary to know the meaning of term in the algebraic expression.
To simplify any algebraic expression we apply the rule:
Let's take the following example:
This expression consists of six terms:
Term 1 is : , the coefficient is
Term 2 is : , the coefficient is
Term 3 is : , the coefficient is
Term 4 is : , the coefficient is
Term 5 is : , the coefficient is
Term 6 is : , the coefficient is
We note that all terms have one of the variables or . To simplify this expression, now it's possible to combine like terms of the variable parts and (combining like terms).
So the simplified expression is:
Let's take the following example:
This expression consists of eight terms:
Term 1 is: , the coefficient is
Term 2 is: , the coefficient is
Term 3 is: , the coefficient is
Term 4 is: , the coefficient is
Term 5 is: , the coefficient is
Term 6 is: , the coefficient is
Term 7 is: , the coefficient is
Term 8 is: , the coefficient is
We note that all terms have one of the variables , , or . To simplify this expression, now it's possible to combine like terms of the variable parts , , and .
So the simplified expression is:
Removal of symbols of grouping is governed by the following rules.
In this example, we take a complex "term" (in parentheses) and try to simplify it using the same rule we saw earlier.
Let's take the following example:
We note that all terms have one of the variables or . To simplify this expression, now it's possible to combine like terms of the variable parts and (combine like terms).
So the simplified expression is:
So as you can see, the most important thing in this simplification, to applying combine like terms, is finding the common variable in terms of the expression. As you also note, this terms can be simple and it can be complex. I hope you have benefited from this explanation.