1.2 Algebraic Expressions & Models
xpression: consists of numbers, operations, and grouping symbols.
numerical eexpression
xpression
25 = 2 i 2 i 2 i 2 i 2
Here 2 is the base and 5 is the exponent or power.
Exponents are used to represent repeated multiplication.
Simplifying Powers
( −2)4 = ( −2) i ( −2) i ( −2) i ( −2) = 16
−24 = − (2 i 2 i 2 i 2) = −16
NOTE: Parentheses make a BIG difference in answers. Order of Operations is a process
of HOW to simplify so everyone has the same answer.
Order of Operations
Operations
Recall: Please Excuse My Dear Aunt Sally
1.) Undo any grouping symbols – parentheses, absolute value, braces, brackets
2.) Evaluate any exponents / powers
3.) Do multiplication and division as they appear left to right
4.) Do addition and subtraction as they appear left to right
Ex:
Ex: Evaluate.
a.) – 8 + 5(1 – (–3))3 =
b.) 52 – 6(2 + (–1))4 =
variable: letter used to represent an unknown quantity
xpression:: an expression involving variables
algebraic eexpression
xpression
Ex: Evaluate – 4x 2 + 6x – 5 when x = –3
Ex:
Ex: You have $55 to buy DVD’s that cost $12 each. Write an expression for how
much money you have left after buying n discs. Evaluate the expression
when n = 3 and n = 4.
Simplifying Algebraic Expressions
2x 3 + 2x + 7x – 12
terms: values between + and – signs
coefficient
oefficient: number in front of any variable
like terms
terms
erms:: terms with exactly the same variable (7x and 2x)
erms: terms without a variable
constant tterms
erms
Ex:
Ex: Simplify, combining like
like terms
terms.
rms.
a.) 2x 3 + 2x + 7x – 12 =
b.) 6m 2 – 12m – 7m 2 =
c.) 3(x – 2) – 5(x – 8) =