1 2 Evaluate and Simplify Algebraic Expressions Numeric

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: 7³ 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 3 x • Coefficient= # in front of a variable (part of the term) 3 x • Constant = a term without a variable (plain #) 3 x -4 y + 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 + 7² · (5 – 3) • 2. 2(-1)⁴ - 4(-2+1)³ (TA) • 3. -4(x)² - 6(x) + 11 if x= -3 (TA)

Expressions vs. Equations Expressions Equations • Can include #’s, operations and variables (letters) • Only ONE side (no =) • Can be simplified using order of operations • 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. 5 x² - 2 x + 8 x² + 10 • 2. 7(x – 3) + 4(x +5) • 3. 4 xy² + 5 x²y – 6 x +3 xy² - 2 x²y + 4 x² -2 x + 5 y • 4. 4 x² - 12 x -9 x² + 3(4 x + 7) • 5. 3(x² + x) – 5(x² - 7) (TA)

Assignment 1 -2 1. 2 pp. 13 -14 # 1, 4, 5, 8, 10, 12, 13, 16 -32 even, 33, 38, 46, 50 Study for quiz on Wed. (8/29) over 1. 1 -1. 2