The distributive property is involving multiplying over grouped subtraction or addition terms.

It is stating that we are multiplying the number that’s outside of the parentheses by each term that’s inside of the parentheses and then add or subtract just as in the original.

**The next lesson: **Combining like terms

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The distributive property in multiplication is a useful property. It lets us rewrite expressions where we are multiplying numbers by a difference or sum.

The distributive property states that the product of a difference or a sum, for example, 6(5 – 2), is equal to the difference or sum of the products, here: 6(5) – 6(2).

6(5 – 2) equals 6(3) = 18

6(5) – 6(2) equals 30 – 12 = 18

This distributive property of multiplication may be used when we’re multiplying a number by a sum. Example: suppose we want to multiply 3 by the sum of the numbers 10 + 2.

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3(10 + 2) equals ?

According to the distributive property, we can add 10 and 2 first and then multiply this by 3, as is shown here: 3(10 + 2) = 3(12) which equals 36.

Alternatively, we can first multiply the addends by 3 (we call this: distributing the 3), and then we can add the products.

The Distributive Properties

For the real numbers a, b, and c counts:

Multiplication will distribute over addition: a(b + c) equals ab + ac

Multiplication will distribute over subtraction: a(b – c) equals ab – ac