# Simplifying Algebraic Expressions

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Simplifying Algebraic Expressions
7.2

Parts of Algebraic Expressions
Term: Separated by addition and subtraction signs. Example: List the Terms: 3x+4y -5 3x,4y,-5

Parts of Algebraic Expressions
Coefficient: The numerical part of a term that contains a variable. Example: Identify the Coefficients: 3x+4y -5 3, 4

Parts of Algebraic Expressions
Like Term: Terms that contain the same variable Example: Identify the Like Terms: 3x +7 +x+2xy The 3x and x are like terms

Parts of Algebraic Expressions
Constant A term without a variable Example: Identify the Constant: 5y +3 +2x 3

Identify the terms, like terms, coefficients, and constants in 2x+3x+4-4x
2,3,-4 Constants: 4

Simplify Algebraic Expressions
An Algebraic Expression is in its simplest terms when it has: no like terms No parenthesis

Simplifying the Expression
Use the Distributive Property Example: 3x +2x =(3+2) x =5x

Ex: Simplify and Justify Steps 4x+6-3x
=4x+6+(-3x) Definition of Subtraction =4x+ (-3x) + 6 Commutative Property =(4+-3)x +6 Distributive Property =X+6 simplify

Ex: Simplify and Justify Your Steps 2m+3-7m-4
=2m +3+(-7m) +(-4) Definition of Subtraction =2m+(-7m)+3+(-4) Commutative Property =(2+-7)m + 3+ (-4) Distributive Property =-5m+ (-1) or -5m -1 Simplify

Ex: Simplify and Justify Your Steps 4a-6-2(a-1)
=4a+(-6)+(-2)[a+(-1)] Definition of Subtraction =4a +(-6) +(-2)(a)+(-2)(-1) Distributive Property =4a +(-6)+(-2a) +2 Simplify =4a +(-2a) +(-6) + 2 Commutative Property =[4+(-2)] a + (-6) +2 Distributive Property =2a + (-4) or 2a -4 Simplify

Total Stamps= Matt+ Lola x+ (x+16) 1x +1x+ 16 (1+1)x +16 2x +16
Lola has 16 more stamps in her collection than Matt. Write an expression in simplest form that represents the total number of stamps in both collections. Matt= x stamps Lola=x + 16 stamps Total Stamps= Matt+ Lola x+ (x+16) 1x +1x+ 16 (1+1)x +16 2x +16

Homework Page 302 (16-44) even