The distributive property is a mathematical and algebraic property that says that multiplying two numbers is the same as multiplying one of those numbers by the sum of the other number's parts. In arithmetic, 50 x 45 is equal to (50 x 40) + (50 x 5). In algebra, the property is shown as x(y + z) = xy + xz.
Using the distributive property in this way helps such number problems to be solved quickly and often without pen and paper. In using the distributive property algebraically, the number on the outside of the parentheses applies to all numbers inside the parentheses.
In the above example, x(y + z) = xy + xz, the variable x is multiplied by both variables in the parentheses, which are y and z. The sign inside the parentheses indicates whether addition or subtraction then occurs. If the equation reads, x(y - z), then the distributive property indicates the equivalent is xy - xz.
If x equals 2, y equals 7 and z equals 5, then:
2(7 + 5) = (2 x 7) + (2 x 5) = 14 + 10 = 24
2(7 -5) = (2 x 7) - (2 x 5) = 14 - 10 = 4