## Presentation on theme: "Adding and Subtracting Expressions"— Presentation transcript:

Section 2.6

Essential Question How can the distributive property
be used to simplify algebraic Expressions?

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.

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

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

3xy -9xy LIKE These are like terms even though
they contain both an x and a y. 3xy -9xy LIKE

These are also like terms.
xy 1 1 yx LIKE We write variables in alphabetical order.

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

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.

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 )

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

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

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

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 )

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

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

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