Distributive Property - Definition and Examples


The distributive property is a property that you can use to multiply a number by a sum or a difference.

For example, to multiply the number 4 by the sum of 6 and 2, you could use the distributive property.

We can express the mathematical phrase "multiply the number 4 by the sum of 6 and 2" as 4(6 + 2)

Using the distributive property, 4(6 + 2) = 4 x 6 + 4 x 2

Notice that as soon as you write 4 x 6 + 4 x 2, you have used the distributive property. 

Similarly, to multiply the number 4 by the difference of 6 and 2, you could use the distributive property.

We can express the mathematical phrase "multiply the number 4 by the difference of 6 and 2" as 4(6 - 2)

Using the distributive property, 4(6 - 2) = 4 x 6 - 4 x 2

Distributive property formula

For every real number a,b, and c,

a(b + c) = ab + ac

(b + c)a = ba + ca

a(b - c) = ab - ac

(b - c)a = ba - ca

We call a(b + c) = ab + ac and (b + c)a = ba + ca  the distributive property of multiplication over addition

We call a(b - c) = ab - ac and (b - c)a = ba - ca the distributive property of multiplication over subtraction.

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