The distributive law is based on the theory of "spreading out." With this law, equations that originally contained parentheses are distributed, or spread out, eliminating the parentheses within the equation. This law combines two concepts -- multiplication and addition -- into one.
The distributive property is used for equations such as 3 + 2(x + 2) = 11. The first step required to solve this problem involves the distributive property. With this law, you must distribute the expressions within the parentheses. To do this, multiply the number outside of it with the information within. In this example, multiply 2 by x, which is 2x, and 2 by 2, which is 4. The equation then reads 3 + 2x + 4 = 11. It can easily be solved now by combining like terms and isolating the variable. This requires several more steps to get to the answer of x = 2.
The most common method used to learn the distributive law is called F.O.I.L. This method is used on math problems that contain two sets of parentheses. It solves the problem by eliminating the parentheses and distributing the information contained within. This method multiplies the first terms, outer terms, inner terms and last terms. For example, the F.O.I.L. method is used to distribute the equation (a + b)(c + d) into the following expression: ac + ad + bc + bd.
Many algebra problems would be considered unsolvable without this property. When a person completes an algebra problem, one of the first steps in solving the problem is most likely using the distributive law. Other laws and principles are also important to learn when studying algebra, including the commutative property and the associative property.