The distributive property is an algebraic expression for multiplying one term or variable with a group of terms or variables within a set of parentheses. The items within the parentheses can contain two or more set terms or variables, for example: a * (b + c).
Distributive properties allow for the removal of the parentheses around the multiple terms or variables as long as the single term outside of these parentheses will multiply each factor. In the statement a * (b + c), "a" would not be multiplied by the total value of b + c. Instead, "a" would be multiplied by each value within the parentheses, making the statement: a * b + a * c = x.
The distributive property can also be used to multiply a series of terms or variables within parentheses without an outside term. For example, in the problem -(b + c), the minus sign would be converted into a -1 since a term without a multiplicative defaults to a value of 1. The formula would then be: -1 * b + -1 * c.
Distributive properties are only used to tie multiplication and addition together into one formula. They cannot be used to add together inside and outside terms. Also, division calculations cannot be distributed over addition within this property. With the distributive property, all values must remain static within the formula. So, in the example a * (b + c), the "c" term cannot switch places with "a."