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What Is the Distributive Property?
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The distributive property is a rule that governs how you can multiply and add numbers
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What Is the Distributive Property?
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Hi my name is Bassem Saad. I'm an associate math instructor and a PhD candidate at UC Davis. I'm here today for About.com to answer the questions, what is the distributive property.
What Is the Distributive Property?

The distributive property is a rule that governs how you can multiply and add numbers at the same time. Note that the order of operations is already a way of handling this but the distribution property gives us another way of getting us the same result. So let a, b, and c be real numbers. And say we want to multiply a times the sum of b and c. You put b and c inside the parentheses because we want to add these numbers first. This expression will be equal to a times b + a times c. That's the same thing as distributing a to each summand inside the expression.
Examples of the Distributive Property?

For example, say we want to multiply 5 times the sum of 4 and 8. If we use the order of operations we have to add the four and the eight first because they're inside the parentheses. That gives us 12. And then 5 x 12 is 60. So with the distributive property we want to multiply 5 times each summand. So we distribute 5 to 4, that's 5 x 4. And then we distribute 5 to 8. That's 5 x 8. Then we add those results. So we've got 5 x 4 is 20, plus 5 x 8, which is 40, equals 60. So it agrees with the order of operations. So in another important example, let x be a variable. We can still use the distributive property to simplify and expression like this; x times the sum of 3 and x. Now you can't combine the sum of 3 and x. This is about as simplified as you can make it. But you can distribute this x onto the other two terms. So you distribute onto the 3 term, that's x times 3. And you distribute the x to the x term. That's x times x. So this whole expression equals 3x + x squared. That was the distributive property.

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