# WRITING EQUIVALENT EXPRESSIONS USING DISTRIBUTIVE PROPERTY

## About "Writing equivalent expressions using distributive property"

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.

## Distributive Property

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)

## Writing equivalent expressions using distributive property - Examples

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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