What is the distributive property?

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baxthum8's profile pic

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

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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`

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flbyrne's profile pic

flbyrne | (Level 3) Assistant Educator

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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

malkaam's profile pic

malkaam | Student, Undergraduate | (Level 1) Valedictorian

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If an expression within a pair of brackets is multiplied by a number, each term within the brackets must be multiplied by that number when the brackets are removed, this is the Distributive Property.

In general, for any 3 integers x, y and z we have x*(y+z)=x * y * x * z. This is called the Distributive law of Multiplication over Addition.

Also, the Distributive Law of Multiplication over Subtraction, that is for any 3 integers x, y and z we have; x*(y-z) = x*y - x*z.

For algebra you can take the following example,

4(a - 2b +3c) = 4a - 8b + 12c. 

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