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An Introduction to Algebra and Simplifying Algebraic Expressions

An Introduction to Algebra and Simplifying Algebraic Expressions

Objective: To use the order of
and distributive
property to simplify expressions.

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.


variablea 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


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

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
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
(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
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


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.


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 .)


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