Simplifying Algebraic Expressions Guide

1 2 evaluate and simplify algebraic expressions n.w

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Learn how to evaluate, simplify, and differentiate between algebraic expressions and equations. Understand the vocabulary, order of operations, and examples to master simplifying expressions effectively.

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1-2: Evaluate and Simplify Algebraic Expressions Numeric expression = numbers, operations and grouping symbols Variable = LETTER used to represent a number Algebraic expression = numbers, operations, grouping symbols and VARIABLES (letters) Algebraic equation= 2 expressions separated with an equal sign. Both sides represent the same value (are equal). Power = A base raised to an exponent Example: 7 means 7 7 7 base is 7 (the number we multiply) exponent is 3 (how many times we multiply the number)

Expression Vocabulary Terms= parts of expressions, separated by addition or subtraction Variable= the letter in a term 3x Coefficient= # in front of a variable (part of the term) 3x Constant = a term without a variable (plain #) 3x -4y + 12

Evaluating Expressions Use ORDER OF OPERATIONS Please Excuse My Dear Aunt Sally Substitute values(# s) in for variables is possible 1) Work inside ( ) or other grouping symbols 2) Apply Powers (exponents) 3) Multiply and Divide from Left to Right 4) Add and Subtract from Left to Right

Examples: Evaluate 1. 1 + 7 (5 3) 2. 2(-1) - 4(-2+1) (TA) 3. -4(x) - 6(x) + 11 if x= -3 (TA)

Expressions vs. Equations Expressions Can include # s, operations and variables (letters) Only ONE side (no =) Can be simplified using order of operations Equations Can include # s, operations and variables (letters) TWO sided; separated with = Each side is an expression that can be simplified separately with order of operations Can be solved by isolating (get it alone) a variable Identities (2 equivalent or = expressions) Can NOT be solved, but may be simplified or evaluated

Simplifying Expressions 1) Simplify inside ( ) if possible 2) Distribute if possible 3) Combine LIKE TERMS Have same variables with same powers Variables and Powers remain the SAME Add or subtract the COEFFICIENTS (# s out front) Follow these steps on EACH side of an equation first BEFORE solving an equation

Examples: Simplify the Expressions 1. 5x - 2x + 8x + 10 2. 7(x 3) + 4(x +5) 3. 4xy + 5x y 6x +3xy - 2x y + 4x -2x + 5y 4. 4x - 12x -9x + 3(4x + 7) (TA) 5. 3(x + x) 5(x - 7) (TA)