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**Simplifying Algebraic Expressions**

7.2

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**Parts of Algebraic Expressions**

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

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**Parts of Algebraic Expressions**

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

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**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

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**Parts of Algebraic Expressions**

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

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

2,3,-4 Constants: 4

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**Simplify Algebraic Expressions**

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

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**Simplifying the Expression**

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

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**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

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**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

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**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

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**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

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Homework Page 302 (16-44) even

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