Distributive property: Whole number coefficients

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

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

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