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 :

Example 2 :

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

Solution :

Example 3 :

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

Solution :

7(x - 3)  =  7x - 7(3)

7(x - 3)  =  7x - 21

Example 4 :

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

Solution :

2(2x - 5)  =  2(2x) - 2(5)

2(2x - 5)  =  4x - 10

Example 5 :

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

Solution :

3(x - 5)  =  3x - 3(5)

3(x - 5)  =  3x - 15

Example 6 :

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

Solution :

5x + 25  =  5x + 5(5)

5x + 25  =  5(x + 5)

Example 7 :

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

Solution :

7y + 5y  =  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)

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