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**Adding and Subtracting Expressions**

Section 2.6

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**Essential Question How can the distributive property**

be used to simplify algebraic Expressions?

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Vocabulary Expression: Combining numbers, variables and addition and subtraction symbols. Does not contain an equal sign. ( 3x + 4 ) + ( 5x + 2 ) Constant: means the same, as fixed. That is, not changing or moving. Coefficient: number sitting before the variable. Term: Parts of an expression separated by + or – signs Like Terms: Terms that contain the SAME form of variable(s) Variables: letter representing a quantity.

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**4x 8x2 unlike Different types of variables are unlike terms.**

To be like terms, the variable part is what has to be the same, not the numbers. unlike

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**2xy - x2y 1 unlike Different types of variables are unlike terms.**

The variable part is what has to be the same, not the numbers. unlike

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**3xy -9xy LIKE These are like terms even though**

they contain both an x and a y. 3xy -9xy LIKE

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**These are also like terms.**

xy 1 1 yx LIKE We write variables in alphabetical order.

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**xy yx LIKE 5 -3 Even if we put numbers in front**

(coefficients) of each variable, they are still like terms. xy yx LIKE 5 -3

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**Distribute Property: To multiply out the parts of an expression**

( 5a + 11 ) – ( 12a – 24 ) ( 3x + 4 ) + ( 5x + 2 ) Simplified: when all like terms have been combined and all parentheses have been removed.

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**Examples Distribute + sign**

2. ( 8x – 2y ) + ( 5x + 6y ) 1. ( 3x + 4 ) + ( 2x – 1 ) 3. ( 3x + 2 ) + ( 4x + 3 ) 4. ( 2b – 3c ) + ( 10b + 4c ) 5. ( 3x + 6 ) + ( -4x + 5 ) 6. ( 4x – 3y ) + ( 2x + 2y )

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**Practice Copy problem Show Combine like terms Simplify**

Page 92 numbers 25, 26, 28, 30, 31 Page 743 Lesson 2.6 numbers 34, 35 Copy problem Show Combine like terms Simplify

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Math Starter ( 3d + 1 ) + ( -4d – 3 ) + ( 5d – 6 )

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**Homework answers 7r + 6r + 2s + 3s 9k + 11k + 2j – 2j 20K**

-1x + 2x + 2y + 3y 1x + 5y 4m – 3m – 2n – 4n 1m – 6n r +17r -7 -6 20r - 13

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**Examples Distribute - sign**

1. ( 4b – 2 ) – ( 5b – 3 ) 2. ( 5a + 3b ) – ( 2a + 5b ) 3. ( - 4m + 3 ) – ( - 6m + 3 ) 4. ( 3m + 17n ) – ( 5m + 15n) 5. ( 2x + 3 ) – ( 4x – 1 )

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**Practice Book page 92 numbers 27, 29, 32, 34, 36, 38 Copy problem**

Show Combine like terms Simplify More practice page 743 lesson 2.6

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**Homework answers 29. 5x + 7 -2x + 7 27. 2a – 1 + 5a + 5**

- 4x – 2y -4x – 2y -4x – 4x – 2y – 2y -8x – 4y -7f + 2 – 6f – 3 -7f – 6f + 2 – 3 -13f - 1

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- 5x + 2y- 3x – 2y -5x – 3x + 2y – 2y - 8x 2q q – 5 + 6q – 7 2q + 4q + 6q + 3 – 5 – 7 12q - 9

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