1.8 Simplifying Algebraic Expressions
Learning Objectives:
1. Evaluate algebraic expressions.
2. Identify like terms and unlike terms.
3. Use the Distributive Property.
4. Simplify algebraic expressions by combining like terms.
1. Evaluate algebraic expressions
Definitions:
1.
A _________________________is any letter that we use to represents any number from a set of
numbers.
2. A ____________________is either a fixed number or a letter or symbol that represents a fixed number.
3.
An __________________________________ is any combination of variables, constants, grouping symbols
and mathematical operations such as addition, subtraction, multiplication, division and
exponents.
4.
To ____________________________________________, substitute a numerical value for each variable into
the expression and simplify the result.
Example 1. Evaluate each expression.
1.
2 p2 + 5p − 1
2.
(x + y )
2
2
for p = −1
for x = 3 and y = −2
2. Identify like terms and unlike terms
Definitions:
1.
A _______________ is a constant or the product of a constant and one or more variable raised to a
power.
2.
The ___________________ of a term is the numerical factor of the term.
1
3.
____________________________ are terms that have the same variable factor(s) with the same
exponent(s).
Example 2. Identify the terms and then name the coefficient of each term:
3x 2 −
4x
5
Example 3. Determine if the terms are like or unlike.
1. 3 and 7
2.
4a 2 and − 7a 2
3.
− 3r 2 s and − 3rs 2
3. Use the Distributive Property
Distributive Property
1. a (b + c ) = ab + ac
where a, b and c are any real numbers.
Example 4.
1.
2.
− a (b + c ) = − ab − ac
Use the distributive property to remove the parentheses.
− (2 x − 3 y )
2.
(4 x + 2 x )5
2
4. Simplify algebraic expressions by combining like terms
Example 5. Simplify each expression by combining like terms.
1.
4 x − 3( y − 6 ) + 3 y + 4 x
2.
3 + 2(4.9 − 5.2 x )
2
3.
3
3
y− y
7
4
4.
1
(− 4 x + 6) − 2 (9 x − 18)
2
3
3