Distributive property: Whole number coefficients

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Definition

The distributive property of multiplication states that when multiplying a number by the sum/difference of 2 numbers, the final value is equal to the sum/difference of each addend multiplied by the third number.

For any three numbers a, b and c

a (b + c) = ab + ac

a (b c) = ab ac

Example 1

Use the distributive property to remove the parentheses.

7(p + 3)

Solution

Step 1:

The distributive property of multiplication tells us that

For any three numbers a, b and c

a (b + c) = ab + ac

a (b c) = ab ac

Step 2:

Using distributive property of multiplication:

7(p + 3) = 7(p) + 7(3) = 7p + 21

Example 2

Simplify the following using distributive property of multiplication:

14(5x 4)

Solution

Step 1:

The distributive property of multiplication tells us that

For any three numbers a, b and c

a (b + c) = ab + ac

a (b c) = ab ac

Step 2:

Using distributive property of multiplication:

14(5x 4) = 14(5x) 14(4) = 70x 56