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Simplifying algebraic expressions by Combining Like Terms

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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.

Note:

A term is every algebraic expression (simple or complex) between the (+) and (-) signs.

To simplify any algebraic expression we apply the rule:

Note:

Like terms with common variable part can be combined and simplified by adding (or substracting) the coefficients of this terms.

Simplifying a simple algebraic expression

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).

  • For we have :
  • For we have :

So the simplified expression is:

Simplifying an algebraic expression with powers

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 .

  • For we have :
  • For we have :
  • For we have :
  • For we have :

So the simplified expression is:

Simplifying an algebraic expression with symbol of grouping

Removal of symbols of grouping is governed by the following rules.

Note:

  1. If a sign precedes a symbol of grouping, this symbol of grouping may be removed without affecting the terms contained.
  2. If a sign precedes a symbol of grouping, this symbol of grouping may be removed if each sign of the terms contained is changed.
  3. If more than one symbol of grouping is present, the inner ones are to be removed first.

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).

  • For we have :
  • For we have :

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.