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What is the Distributive Property

Updated on December 6, 2012

The Distributive Property

The Distributive Property is part of an expression that contains parentheses, we use the property in order to remove the parenthesis and simply the expression.

In the first example 3 is outside of the parentheses and needs to be distributed to each term within the parentheses. The 3 is multiplied by x and by 2y in order to get rid of the parentheses and simplify the expression.


Distributive Property
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Distributive Property

The next example shows how a problem can be simplified using the distributive property. I used the previous example at the first term of the parentheses. I added a second item with parentheses with the same exponents.

By using the distributive property to get rid of the parentheses we can then add like terms together in order to create a simplified item.

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This example uses terms with parentheses

There are two terms in the first parentheses and two in the second.

First inner, outer, Second inner, outer.

X is the first term multiply it by the inner term and then the outer.

3y is the second term, multiply it by the inner term and then the outer.

Combine like terms -xy & 6xy are considered like terms. Together they are 5xy.

The distributive property allows us to simplify the expression

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Square Parentheses

The same principal and theory can be applied to squared parentheses.

Rewrite the problem with two of the same terms and repeat the previous process

First: inner, outer, Second: inner, outer

Note: I included the xy and yx reversal so that you notice that those are the same terms. Remember the commutative property of multiplication


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