SIMPLIFY VARIABLE EXPRESSIONS USING PROPERTIES

Simplify the following variable expressions :

Example 1 :

(y + 3) + 8

Solution :

= (y + 3) + 8

= y + 11

Example 2 :

3(4m)

Solution :

= 3(4m)

= 12m

Example 3 :

(2 + x) + 5

Solution :

= (2 + x) + 5

= x + 5

Example 4 :

(7p)(5)

Solution :

= (7p)(5)

= 35p

Example 5 :

4(2x + 3 - 5x) + 2(3x - 4)

Solution :

= 4(2x + 3 - 5x) + 2(3x - 4)

Apply distributive property.

= 8x + 12 - 20x + 6x - 8

Combine the like terms.

= 8x + 6x - 20x + 12 - 8

= -6x + 4

Example 6 :

5(2x - 3) + 7(2 - 5x) - (3x - 4)

Solution :

= 5(2x - 3) + 7(2 - 5x) - (3x - 4)

Apply distributive property.

= 10x - 15 + 14 - 35x - 3x + 4

Combine the like terms.

 = 10x - 35x - 3x - 15 + 14 + 4

= -28x + 3

Example 7 :

-8(-5b + 7) + 5b - 3b

Solution :

= -8(-5b + 7) + 5b - 3b

Apply distributive property.

= 40b - 56 + 5b - 3b

Combine the like terms.

= 40b + 5b - 3b - 56

= 42b - 56

Example 8 :

-4p - (1 - 6 p)

Solution :

= -4p - (1 - 6p)

Apply distributive property.

= -4p - 1 + 6p

Combine the like terms.

= -4p + 6p - 1

= 2p - 1

Example 9 :

4 - 5(-4n + 3) - (3 - 2n)

Solution :

= 4 - 5(-4n + 3) - (3 - 2n)

Apply distributive property.

= 4 + 20n - 15 - 3 + 2n

Combine the like terms.

= 20n  + 2n - 15 - 3 + 4

= 22n - 14

Example 10 :

 2(x + y) + 3(2x + 4y)

Solution :

= 2(x + y) + 3(2x + 4y)

Apply distributive property.

= 2x + 2y + 6x + 12y

Combine the like terms.

= 2x + 6x + 2y + 12y

= 8x + 14y

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