SIMPLIFY VARIABLE EXPRESSIONS INVOLVING LIKE TERMS AND THE DISTRIBUTIVE PROPERTY

Distributive Property :

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

Combining Like Terms :

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

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

Example 1 :

Simplify :

6r + 7 - (13 - 7r)

Solution :

=  6r + 7 - (13 - 7r)

=  6r + 7 - 13 + 7r

=  6r + 7r + 7 - 13

=  13r - 6

Example 2 :

Simplify :

-7x - 3x + 2 - (8x + 8)

Solution :

=  -7x - 3x + 2 - (8x + 8)

=  -7x - 3x + 2 - 8x - 8

=  -7x - 3x - 8x - 8 + 2

=  -18x - 6

Example 3 :

Simplify :

4n - 40 - 7(-2n + 2) 

Solution :

  =  4n − 40 - 7(−2n + 2) 

  =  4n − 40 + 14n - 14 

  =  4n + 14n − 40  - 14

  =  18n  − 54

Example 4 :

Simplify :

38 + 7k - 8(k + 4)

Solution :

  =  38 + 7k - 8(k + 4)

  =  38 + 7k - 8k - 32

  =  38 - 32 + 7k - 8k 

  =  6 - k

Example 5 :

Simplify :

3(1 - 3x) - 2(-4x + 7)

Solution :

=  3(1 − 3x) - 2(−4x + 7)

=  3 − 9x + 8x - 14

=  − 9x + 8x - 14 + 3

=  − x - 11

Example 6 :

Simplify :

2x + 3 - (5x - 2)

Solution :

=  2x + 3 - (5x - 2)

=  2x + 3 - 5x + 2

=  2x - 5x + 2 + 3

=  -3x + 5

Example 7 :

Simplify :

7x - 5x + 2 - (x - 1) 

Solution :

=  7x − 5x + 2 − (x - 1) 

=  7x − 5x + 2 − x + 1 

=  7x - 5x -x + 2 + 1

=  7x - 6x + 3

=  x + 3

Example 8 :

Simplify :

-6n - 20 - 2n - 4(1 + 3n)

Solution :

  =  −6n − 20 − 2n - 4(1 + 3n)

  =  −6n − 20 − 2n - 4 - 12n

  =  −6n − 2n - 12n - 20 - 4

  =  −20n - 24

Example 9 :

Simplify: 

-8n + 4(1 + 5n) - (6n + 14) 

Solution :

  =  -8n + 4(1 + 5n) - (6n + 14) 

  =  -8n + 4 + 20n - 6n - 14 

  =  -8n + 20n - 6n - 14 + 4 

=  -14n + 20n - 10

=  6n - 10

Example 10 :

Simplify : 

7(5a - 4) - 1 - (14 - 8a)

Solution :

  =  7(5a − 4) − 1 - (14 − 8a)

  =  35a - 28 - 1 - 14 + 8a

  =  35a + 8a - 28 - 1 - 14

  =  43a - 43

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