lesson 3.4 expanding algebraic expressionsmscieloflores.weebly.com › ... ›...

13

(6x ! 12)

Method 1 Use a bar model.

2x 4 2x 4 2x 46x ! 12

13

(6x ! 12)

From the bar model,

13

(6x ! 12) " 2x ! 4

Method 2 Use the distributive property.

13

(6x ! 12) " 13

( 6x ) ! 13

( 12 ) Use the distributive property.

Multiply. " 2x ! 4

Lesson 3.4 Expanding Algebraic Expressions

Example

Arrange the bar model for 6x ! 12 into 3 equal groups to find one third of (6x ! 12).

1. 12

(4x ! 6)

Method 1 Use a bar model.

2x 3 2x 34x ! 6

12

(4x ! 6)

From the bar model,

12

(4x ! 6) " !

Method 2Use the distributive property.

12 (4x ! 6) "

12

( ) ! 12

( )

" !

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MIF_Reteach C2_Ch03.indd 73 15/12/11 1:49 AM

0.6(0.3x ! 5)

0.6(0.3x ! 5) " 0.6[0.3x # (!5)] Rewrite subtraction as a sum.

Use the distributive property.

Multiply.

Rewrite the expression.

" 0.6( 0.3x ) # 0.6( !5 )

" 1.8x # ( !3 )

" 1.8x ! 3

Example

2. 14

(12x # 16) 3. 15 (10x # 35)

4. 13 (8m # 6) 5.

18 (7 # 3n)

6. 0.3(3x # 7) 7. 0.9(2.1y ! 2)

0.3(3x # 7)

" 0.3( ) # 0.3( )

" #

8. 1.5(0.4p # 2.1) 9. 1.3(3w ! 1.1)

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74 Chapter 3 Lesson 3.4


a) ! "2 14

18

a⎛⎝⎜

⎞⎠⎟

! "2 14

18

a⎛⎝⎜

⎞⎠⎟ ! ("2)

14

a # ("2)

18


Multiply.


757575757575757575757575 !

"12

a #

"14

757575757575757575757575 !

"12

a #

14

b) ! ! "13

2 6( )x y

! ! "13

2 6( )x y ! " 13

("2x) # "13

⎛⎝⎜

⎞⎠⎟

(6y) Use the distributive property.

Multiply.


!

23

x #

("2y)

!

23x

" 2y

c) "(2.5m " 3.6)

"(2.5m " 3.6) ! "1[ 2.5m # (

"3.6 )] Rewrite the expression.


Multiply.

757575757575757575757575 ! "1( 2.5m ) # ("1)( "3.6 )

757575757575757575757575 !

"2.5m #

3.6

Example

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16. 4(2d ! 3f ) ! 6d " 4(2d ) ! 4( ) ! Use the distributive property.

Multiply.

Group like terms.

Simplify.

" ! !

" ! !

" !

10. #3(#5a # 6) 11. #14

(4y ! 7)

" #3[#5a ! ( )] " # 14

( ) ! #14

⎛⎝⎜

⎞⎠⎟ ( )

" #3( ) ! (#3)( ) " !

" "

12. ! "3 2 13

x⎛⎝

⎞⎠ 13. # #5 3

102a⎛

⎝⎜⎞⎠⎟

14. ! ! "12

4 13

x⎛⎝

⎞⎠ 15. #0.6(#7x # 9)

3(a ! 2b) # 4b

3(a ! 2b) # 4b " 3( a ) ! 3( 2b ) # 4b Use the distributive property.

Multiply.

Simplify.

" 3a ! 6b # 4b

" 3a ! 2b

Example

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17. 4(g ! 5h) ! 3h 18. 6x ! 3(7y ! x)

! !3 23

2 4x x⎛⎝

⎞⎠ "

! !3 23

2 4x x⎛⎝

⎞⎠ " " #3[

23

x ! ( #2 )] ! 4x Rewrite the expression.


Multiply.

Group like terms.

Simplify.

" (#3)23

x ! (#3)( #2 ) ! 4x

" #2x ! 6 ! 4x

" #2x ! 4x ! 6

" 2x ! 6

Example

19. #2(1.5y # 1) # 2y

#2(1.5y # 1) # 2y " #2[1.5y ! ( )] # 2y Rewrite the expression.


Multiply.

Group like terms.

Simplify.

" #2( ) ! (#2)( ) #

" ! #

" # !

" !

20. # # #4 14

2 3g g⎛⎝

⎞⎠ 21. #4(1.5m # 3) ! 6m

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2(3a ! 1) " (b ! 2)

2(3a ! 1) " (b ! 2)

# 2(3a ! 1 ) ! ( "1 ) ( b ! 2 ) Rewrite the expression.


Multiply.

Group like terms.

Remove parentheses and simplify.

# 2( 3a ) ! 2( 1 ) ! ("1)( b ) ! ("1)( 2 )

# 6a ! 2 ! ("b) ! ("2)

# 6a ! ("b)

# 6a " b

Example

22. 3(2a ! 4) " 2(b " 2)

3(2a ! 4) " 2(b " 2)

# 3(2a ! 4) ! ( )( " ) Rewrite the expression.


Multiply.

Group like terms.

Remove parentheses and simplify.

# 3( ) ! 3( ) ! ( )( ) ! ( )( )

# ! ! !

# ! ! !

#

23. 4 12

3 4x y! !⎛⎝⎜

⎞⎠⎟ ( )" 24. "2(m " 4) " 2(2n " 2)

25. 3(d ! 7) " 2(3g " 2) 26. "6(p " 3) " (5q " 4)

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