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Introduction to Algebra Vocabulary Identifying Parts of an Algebraic Expression Distributive Property of Multiplication Expression: a group of terms. Contains 3 things: • Numbers • Operations • Variables • ***DOES NOT CONTAIN AN EQUAL SIGN!! VARIABLE A LETTER/SYMBOL THAT REPRESENTS AN UNKNOWN NUMBER Every variable has a coefficient. 1-9 Simplifying Algebraic Expressions In the expression 7x + 9y + 15, 7x, 9y, and 15 are called terms. A term can be a number, a variable, or a product of numbers and variables. Terms in an expression are separated by + and –. 7x + 5 – 3y2 + y + x 3 term term term term term In the term 7x, 7 is called the Coefficient coefficient. A coefficient is a number that is multiplied by a variable in an algebraic expression. A variable by itself, like y, has a coefficient of 1. So y = 1y. Course 2 Variable Identifying parts of an expression. Constant: the term without a variable. 3, 6, 5, 32 Like Terms: terms with the same variable factors, but may have different coefficients. 2 3x, 6 x, 21x y, 0.75 y, 126 y, 32 y 5 4ab 3 , 9ab 3 , 7b 3 a 1-9 Simplifying Algebraic Expressions Like terms are terms with the same variable raised to the same power. The coefficients do not have to be the same. Constants, like 5, 1 , 2 and 3.2, are also like terms. Like Terms Unlike Terms Course 2 w and w 5 and 1.8 7 5x2 and 2x 6a and 6b 3.2 and n The exponents The variables Only one term contains a are different. are different variable 3x and 2x 1-9 Simplifying Algebraic Expressions Additional Example 1: Identifying Like Terms Identify like terms in the list. 3t 5w2 7t 9v 4w2 8v Look for like variables with like powers. 3t 5w2 7t 9v Like terms: 3t and 7t 4w2 8v 5w2 and 4w2 9v and 8v Helpful Hint Use different shapes or colors to indicate sets of like terms. Course 2