Download 1.8 Simplifying Algebraic Expressions

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. 2 p2 + 5p − 1 (x
2
+ y) 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). 4x
Example 2. Identify the terms and then name the coefficient of each term: 3x 2 −
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 2. − a (b + c ) = − ab − ac where a, b and c are any real numbers. Example 4. Use the distributive property to remove the parentheses. 1. − (2 x − 3 y ) 2. (4 x
2
+ 2 x )5 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