1.2.3 Simplifying Expressions (continued) Example 2 Using the Distributive Property with Mental Math By the Distributive Property, the product of a value and a sum (or difference) is equal to that value multiplied by each of the values being added (or subtracted). • Distributive Property (addition): a ( b + c ) = ab + ac • Distributive Property (subtraction): a ( b − c ) = ab − ac The Distributive Property can be used to write an expression in a way that makes mental math easier.
Example 3 Combining Like Terms
Terms (the parts of the expression separated by addition or subtraction) can be a number, a variable, or a product of a number and a variable. In the product of a number and a variable, the number is called the coefficient. For example, 3 x + 5 + x has three terms, 3 x , 5, and x . The coefficient of 3 x is 3. The coefficient of x is 1, because x = 1 x . Terms with variables are like terms if they have exactly the same variable (or variables) to exactly the same power. Algebraic expressions can be simplified by combining (adding or subtracting) the like terms. Like terms with variables are combined by adding (or subtracting) their coefficients. Terms without variables are called constants. Constants are always like terms.
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