SIMPLIFY VARIABLE EXPRESSIONS INVOLVING LIKE TERMS

In order to simplify (addition or subtraction) algebraic expressions, we need to combine like terms. 

Before we do "combining like terms", first let us come to know what are like terms and unlike terms. 

Like Terms or Similar Terms : 

Like terms are the terms which have the same variables with same exponent for each variable.

7x, 3x, - 4x are the examples of like terms

Unlike Terms or Dissimilar Terms : 

Unlike terms are the terms which have same variables or different variables. 

If they have same variables, the exponents will not be same. 

 9x², 5xy, - 4xy², y, 6 are the examples of unlike terms

Using Distributive Property :

Whenever we have a number or variable or an algebraic term out side the the parentheses, we have to multiply that particular term with the terms inside the parentheses and simplify.

Example 1 :

Simplify : 

-2(x - 9) + 4 (x + 7)

Solution :

In order to simplify the above expression, we need to use the distributive property.

  =  −2(x − 9) + 4 (x + 7)

  =   -2x + 18 + 4x + 28

  =  -2x + 4x + 18 + 28

  =  2x + 46

Example 2 :

Simplify :

6x - 3(2 - 3x)

Solution :

In order to simplify the above expression, we need to use the distributive property.

  =   6x − 3(2 − 3x)

  =    6x − 6 + 9x

  =  6x + 9x - 6

  =  15x - 6

Example 3 :

Simplify :

- 6 + 9 (8 - 2b) 

Solution :

In order to simplify the above expression, we need to use the distributive property.

  =   −6 + 9 (8 − 2b) 

  =    -6 + 72 -  18b

  =  66 - 18 b

Example 4 :

Simplify :

4(x - 10) - 6(x - 4)

Solution :

In order to simplify the above expression, we need to use the distributive property.

  =   4(x − 10) − 6(x − 4)

  =   4x - 40 - 6x + 24

  =  4x - 6x - 40 + 24

=  -2x - 24

Example 5 :

Simplify :

10(9 + 8x) - 6(7x + 9)

Solution :

In order to simplify the above expression, we need to use the distributive property.

  =   10(9 + 8x) − 6(7x + 9)

  =   90 + 80 x  - 42x - 54

  =  90 - 54 + 80 x  - 42x

=  36 + 38x

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