In algebra the fundamental building blocks of all algebra problems are math
expressions. Math expressions come in 2 primary forms.
Numeric Expressions:
Expressions containing numbers and or operations symbols.
Algebraic Expressions:
Algebraic expressions are math expressions that contain one
or more variables. ( A variable is what we use a symbol,
usually a letter used to represent on or more numbers)
1
In algebra, one of the most important basic skills is to be able to simplify numeric or
algebraic expressions. Simplifying is a process we use to rewrite the expression in an
equivalent but simpler form. For numeric expressions that form is a simpler number. For
Algebraic expressions the simpler form will be a simpler algebraic expression or a numeric
expression. In either case, we must all simplify in the same order.
PEMDAS (Please Excuse My Dear Aunt Sally)
This is a memory device often referenced when simplifying expressions. It implies the
following simplification process.
P (Please) – Simplify any expression contained in any grouping symbols first.
E (Excuse) – Simplify any expression with an exponent attached.
M/D (My/Dear, Dear/My) – Simplify all multiplication and division in the expression from
left to right.
A/S (Aunt/Sally, Sally/Aunt) – Simplify all addition and subtraction in the expression from
left to right.
Simplification is complete in numeric expressions when the expression is a single number.
Simplification is complete in an algebraic expression when the expression is cleared of all
parenthesis and all like terms have been combined.
Examples:
(5  3)2
5
2
3.
22 
5.
2( x  1)2  ( x  1)
4.
2
Evaluating an expression means to give a numeric value to an algebraic expression by first
simplifying the expression and the replacing the remaining variables with their given
values.
Example: Evaluate the given expression if x = 2 and y = -3.
4( x  2)  3 5  y  4 x  8
Practice: Simplifying Expressions
Simplify the given numeric or algebraic expressions
1.
2.
3.
5. 42  (6  10)  52  3
4.
Simplify the given algebraic expression
6.
7.
8.
2( x  y)  ( x  y)  ( x  2)2
3
Evaluate the following
9.
10.
11.
3( x  1)  4 x  3  x
let x  579
4