*Last Updated on February 15, 2024.*

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.

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### Video Transcription

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 is stating that the product of a difference or a sum, for example, 6(5 – 2), equals 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

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

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

When working with real numbers a, b, and c, the following applies:

Multiplication distributes over addition: so a(b + c) is equal to ab + ac

Multiplication distributes over subtraction: so a(b – c) is equal to ab – ac

Again, the distributive property involves multiplying over grouped subtraction or addition terms.

It states we multiply the number that’s outside of the parentheses by each term or number that’s inside of the parentheses. Then, we subtract or add just like in the original.

The distributive property in multiplication is very useful as it allows us to rewrite expressions where we multiply numbers by a sum or difference.