Distributive Property of Multiplication over Addition and Subtraction

left arrowDistributive property
no left arrowTry it with numbers
no left arrowVisual Representation
no left arrowno left arrowVisual Representation 2
no left arrowGuided practice 1
no left arrowWorksheet 1
no left arrowGeometric Representation
no left arrowWhy do we need to know?
no left arrowDistributing variables
no left arrowGuided practice 2
no left arrowWorksheet 2
no left arrowFactoring
no left arrowGuided practice 3
no left arrowWorksheet 3

What is the Distributive Property?

The distributive property of multiplication over addition and subtraction is stated mathematically as a·(b+c) = a·b+a·c. Here is a diagram that shows what we mean by distribute.
a(b+c)=ab+ac means the a is distributed across the addition to the b and c.
Notice that the a is distributed across the addition to b and c. Take another look. See where the a, b, and c start out and end up.
In a(b+c)=ab+ac, the a ends up next to both the b and c.

The distributive property also works with subtraction. a·(b-c) = a·b-a·c