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# What is the distributive property?

mfay8995 | eNotes Newbie

Posted November 15, 2013 at 11:08 PM via iOS

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What is the distributive property?

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flbyrne | (Level 3) Assistant Educator

Posted November 16, 2013 at 12:26 AM (Answer #1)

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The distributive property is the ability of multiplication to "distribute" over another operation inside parenthesis. Multiplication distributes over addition or subtraction, such that x(a+b) = xa + xb.

This means we can distribute the factor outside the set of parenthesis to each item inside, and then add the results.

Example: 5(2+3) is equivalent to 5*2 + 5*3 because the multiplication by five was distributed across the addition inside the parenthesis.

Division is not distributive over addition or subtraction

Example: 10/(5-3)`!=` `10/5-10/3`

The Distributive Property can be used in arithmetic to make multiplication easier, breaking up one of the numbers and multiplying two parts separately and then add the products.

Example: 3*37=(3x30)+(3x7)

In Algebra, the Distributive Property helps you simplify expressions with parenthesis.

Example: a(b+c) = ab+ac

baxthum8 | High School Teacher | (Level 3) Associate Educator

Posted November 16, 2013 at 10:50 PM (Answer #2)

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The Distributive Property lets you multiply a sum by multiplying each addend separately and then add the products.

The Distributive Property is handy to help you get rid of parentheses.

a(b + c) = ab + ac

To multiply in algebra, you'll use the distributive law:
`3x(x+5)= `

`3x(x) + 3x(5)=`

`3x^2+15x`

Sources:

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