The distributive property in algebra simplifies equations by altering them from their original form a(b+c) to the easier-to-solve form of ab + ac. The distributive property helps students utilize the order of operations and distributive law when using real numbers with variables.
Following the order of operations in mathematics, or PEMDAS, the equation a(b+c) requires users to first add the numbers in the parenthesis before multiplying them by "a." Following the order of operations is easy when all real numbers are present, but it becomes more complicated once an algebraic variable is introduced. It is at this point that users require the use of the distributive property to simplify the problem.
For example, in arithmetic, the problem proceeds as follows:
However, when presented with a variable, this changes. First, the problem is easier to understand without the parenthesis because it more clearly isolates x:
- 2*4 + 2*3x
- 8 + 6x
Second, when the original problem of 2(4+3x) is one-half of an equation, converting it to 8+6x using the distributive property allows users to easily solve for x. For example:
- 2(4+3x) = 20
- 2*4 + 2*3x = 20
- 8 + 6x = 20
- 6x = 12
- x = 2