**Simplify variable expressions using properties :**

We use the following properties to simplify variable expressions.

(1) Distributive property

(2) Combining the like terms

**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 the 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.

Note :

After we use distributive property, we combine like terms.

Let us look into some example problems to understand the above concept.

**Example 1 :**

Simplify the following expression

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

**Solution :**

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

Let us distribute the number outside the parentheses.

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

Now we need to combine the like terms, for that let us write x terms in one side and constants in other side.

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

= 14x - 20x + 4

= - 6x + 4

Hence the answer is -6x + 4.

**Example 2 :**

Simplify the following expression

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

**Solution :**

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

Let us distribute the number outside the parentheses.

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

Now we need to combine the like terms, for that let us write x terms in one side and constants in other side.

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

= 10x - 38x - 15 + 18

= - 28x + 3

Hence the answer is -28x + 3.

**Example 3 :**

Simplify the following expression

−8(−5b + 7) + 5b - 3b

**Solution :**

= −8(−5b + 7) + 5b - 3b

Let us distribute the number outside the parentheses.

= 40b - 56 + 5b - 3b

Now we need to combine the like terms, for that let us write x terms in one side and constants in other side.

= = 40b + 5b - 3b - 56

= 45b - 3b - 56

= 42b - 56

Hence the answer is 42b - 56.

**Example 4 :**

Simplify the following expression

−4p − (1 − 6 p)

**Solution :**

= −4p − (1 − 6p)

Let us distribute the number outside the parentheses.

= −4p − 1 + 6p

= -4p + 6p - 1

= 2p - 1

Hence the answer is 2p - 1.

**Example 5 :**

Simplify the following expression

4 − 5(−4n + 3) - (3 - 2n)

**Solution :**

= 4 − 5(−4n + 3) - (3 - 2n)

Let us distribute the number outside the parentheses.

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

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

= 22n - 18 + 4

= 22n - 14

Hence the answer is 22n - 14.

**Example 6 :**

Simplify the following expression

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

**Solution :**

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

Let us distribute the number outside the parentheses.

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

Now we need to combine the like terms, for that let us write x terms in one side and y terms in other side.

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

= 8x + 14y

Hence the answer is 8x + 14y.

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