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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