**Writing equivalent expressions using distributive property :**

Already we know that multiplication is distributive over addition and subtraction.

We can use this distributive property to write equivalent algebraic expressions.

Multiplying a number by a sum or difference is the same as multiplying by each number in the sum or difference and then adding or subtracting.

**Examples : **

6(2 + 4) = 6(2) + 6(4)

8(5 - 3) = 8(5) - 8(3)

**Example 1 :**

Use distributive property to write an expression that is equivalent to 3(10 + 2).

**Solution :**

Using distributive property, the expression equivalent to 3(10 + 2) is **3(10) + 3(2)**

**Example 2 :**

Use distributive property to write an expression that is equivalent to 5(6 - 3).

**Solution :**

Using distributive property, the expression equivalent to 5(6 - 3) is **5(6) - 5(3)**

**Example 3 :**

Use distributive property to write an expression that is equivalent to 7(x - 3).

**Solution :**

Using distributive property, the expression equivalent to 7(x - 3) is **7x - 21**

**Example 4 :**

Use distributive property to write an expression that is equivalent to 2(2x - 5).

**Solution :**

Using distributive property, the expression equivalent to 2(2x - 5) is **4x - 10**

**Example 5 :**

Use distributive property to write an expression that is equivalent to 3(x - 5)

**Solution :**

Using distributive property, the expression equivalent to 3(x - 5) is **3x - 15**

**Example 6 :**

Use distributive property to write an expression that is equivalent to 5x + 25

**Solution :**

5x + 25 = 5x + 5(5) = 5(x + 5)

Using distributive property, the expression equivalent to 5x + 25 is **5(x + 5)**

**Example 7 :**

Use distributive property to write an expression that is equivalent to 7y + 5y

**Solution :**

7y + 5y = y(7 + 5)

Using distributive property, the expression equivalent to 7y + 5y is **y(7 + 5)**

**Example 8 :**

Use distributive property to write an expression that is equivalent to 0.2y + z

**Solution :**

0.2y + z = 0.2y + 1z

0.2y + z = 0.2y + 0.2(5z)

0.2y + z = 0.2(y + 5z)

Using distributive property, the expression equivalent to 0.2y + z is **0.2(y + 5z)**

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