In arithmetic , we perform mathematical
operations with specific numbers. In
algebra, we perform these same basic
operations with numbers and variables,
which are letters that stand for
unknown quantities .

variable – a symbol, usually a letter, that
represents one or more numbers

algebraic expression – a math phrase with
numbers, variables, and operation symbols

evaluate – substitute and simplify

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

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.

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)

To evaluate 2x - y when x = 5 and y = -3,
replace the variables with their values in
parentheses and simplify.

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

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.

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.

If an expression inside parentheses is
preceded by a “+” sign, then remove
the parentheses by simply dropping
them. For example:

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 .)