# An Introduction to Algebra and Simplifying Algebraic Expressions

 Objective: To use the order of operations and distributive property to simplify expressions. Introduction In arithmetic, we perform mathematical ope rations with specific numbers. In algebra, we perform these same basic operations with numbers and variables , which are letters that stand for unknown quantities. Definitions variable – a symbol , usually a letter, that re presents one or more numbers algebraic expression – a math phrase with numbers, variables, and operation symbols evaluate – substitute and simplify The following are some basic mathematical properties that we will apply: Commutative: a + b = b + a; ab = ba Associative: (a + b) + c = a + (b + c); (ab)c =a(bc) Distributive: a(b + c) = ab +ac a + 0 = a a(0) = 0 a + (-a) = 0 a(1) = a Order of Operations, pg. 202 1. Grouping symbols (parentheses, brackets , fraction bar ) 2. Exponents 3. Multiply and divide in order from left to right. 4. Add and subtract in order from left to right. P.E.M.D.A.S. Please Excuse My Dear Aunt Sally! 1. P – parentheses (any grouping symbols) 2. E – exponents 3. M/D – multiply/divide (left to right) 4. A/S – add/subtract (left to right) Simplify using the Order of Operations. Your Turn: Simplify using the Order of Operations. Evaluating an Expression To evaluate 2x - y when x = 5 and y = -3, replace the variables with their values in parentheses and simplify. Evaluate if x = 2. Simplifying Algebraic Expressions term – a number, a variable, or a product of a number & variable(s) constant – a number that does not change in value coefficient – a numerical factor of a term (the number in front of a variable) like terms – exactly the same variable and power An explanation Terms are always separated by a plus (or minus) sign. For example, the expression 2x - 3y has two terms, 2x and -3y. In this expression, 2 and -3 are constants, x and y are variables with 2 being the coefficient of x and -3 the coefficient of y. The expression 2x +3y -5 has 3 terms. Example: Simplify each expression by combining like terms. Distributive Property If an algebraic expression that appears in parentheses cannot be simplified, then multiply each term inside the parentheses by the factor preceding the parentheses. Then combine like terms. Distributive Property Practice Parentheses If an expression inside parentheses is preceded by a “+” sign, then remove the parentheses by simply dropping them. For example: 3x + (4y + z) = 3x + 4y + z. Parentheses If an expression in parentheses is preceded by a “-” sign then it is removed by changing the sign of each term inside the parentheses and dropping the parentheses. For example, 3x – (4y – z) = 3x – 4y + z. (This is like distributing a negative one .) Simplify
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