WARMUPS

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WARMUPS

• -5(A B)
• -3(C - 6)
• (A 13)2
• 2X(X Y)
• 3X 2X X 3X

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DISTRI BUTIVE PROPERTY

• CHAPTER 1-5

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WHAT IS THE DISTRIBUTIVE PROPERTY?

• IN WORDS THE SUM OF TWO ADDENDS MULTIPLIED BY A
  NUMBER IS THE SUM OF THE PRODUCT OF EACH ADDEND
  AND THE NUMBER
• GOT THAT!!!!!!!!!!!!

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OK WHAT DOES THAT MEAN
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The Distributive Property Combining Like Terms
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The product of a and (b c)

2(x 5)
2(x) 2(5)
2x 10

a(b c) ab ac
2x 10
(b c)a ba ca
(x 5)2
(x)2 (5)2


y(1 x)


y(1) y(x)
y xy


(1 5x)2
(1)2 (5x)2
2 10x
BACK
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Remember that a factor must multiply each term of
an expression.
Distribute the 3.
(3)(1 x)
(3)(1) (3)(x)
Simplify.
3 3x
(y 5)
(y)(1) (5)(1)
Distribute the 1.
Simplify.
y 5
(1)(7) (1)(3x)
a 1 a
(7 3x)
Simplify.
7 3x
Forgetting to distribute the negative sign when
multiplying by a negative factor is a common
error.
BACK
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Like Terms are expressions that contain the same
variable raised to the same power like 4mn and
7mn.
11x y
8x 3x y
The 8x and 3x are like terms and can be combined.
4x2 2 x2 - 6
4x2 1 x2 2 - 6
Group like terms.
5x2 - 4
Combine like terms.
BACK
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BACK
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Combine like terms with parenthesis
BACK
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Objectives

• Use the Distributive Property to solve equations.
• Solve real-world problems by using multistep
  equations.

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Key Skills
Use the distributive property.
Solve 3(x - 4) 48
Solve 3(x - 4) 48
3 x 3 -4 48
Multiply
Add both sides of the sign.
3x - 12 48
12 12
Divide both sides of the sign by 3.
3x 60
3 3
x 20
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Key Skills
TRY THIS
Use the distributive property.
Solve 5(x 2) 35
Solve 5(x 2) 35
5 x 5 2 35
Multiply
Subtract 10 from both sides of the sign.
5x 10 35
-10 -10
Divide both sides of the sign by 3.
5x 25
5 5
x 5
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Key Skills
Combine like terms that are on the same side of
the sign.
Solve 3y 8 y 6
Solve 3y 8 y 6
2y 8 6
Add 8 to both sides of the sign.
8 8
2y 14
Divide both sides of the equal sign by 2
2 2
y 7
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Key Skills
TRY THIS
Combine like terms that are on the same side of
the sign.
Solve 6y 2 3y 8
Solve 6y 2 3y 8
3y 2 8
Subtract 2 from both sides of
the sign.
-2 -2
3y 6
Divide both sides of the equal sign by 3
3 3
y 2
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Key Skills
Solve
4x -8(x 1) 8
4x -8(x 1) 8
Distribute -8
4x -8 x -8 1 8
Multiply
4x -8x -8 8
4x -8x -8 8
Combine like terms.
-4x -8 8
Add 8 to both sides of the sign.
8 8
-4x 16
Divide both sides of the equal sign by -4
-4 -4
x -4
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Key Skills

• Use the Distributive Property to solve multistep
  equations.

Solve 8x 2(3x 4) 5x 7.
Solve 8x 2(3x 4) 5x 7.
Distributive -2
Multiply.
8x (2)(3x) (2)(4) 5x 7
Combine like terms that are on the same side of
the sign.
8x 6x 8 5x 7
8x 6x 8 5x 7
2x 8 5x 7
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Subtract 2x from both sides of the sign.
2x 8 5x 7
-2x -2x
Add 7 to both sides of the sign.
8 3x -7
7 7
Divide both sides of the sign by 3
15 3x
3 3
5 x
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Key Skills
TRY THIS

• Use the Distributive Property to solve multistep
  equations.

Solve 4y 7(y 6) 5y 2.
Solve 4y 7(y 6) 5y 2.
Distributive -7
4y (7)(y) (7)(6) 5y 2
Multiply.
Combine like terms that are on the same side of
the sign.
4y 7y -42 5y 2
4y 7y -42 5y 2
-3y -42 5y 2
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Add 3y to both sides of the sign.
-3y -42 5y 2
3y 3y
Add 2 to both sides of the sign.
-42 8y -2
2 2
Divide both sides of the sign by 8
-40 8y
8 8
-5 y
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HOMEWORK DO YOU HEAR HANDOUT

• IF YOU CAN DO THESE YOU ARE A SUPER MATHEMATICIAN

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HOMEWORK

• 11. -3 ( 2Y 6)
• 12. -7 ( -3N 2)
• 13. (5Y 8) (-3)
• 14. 2(X Y Z)
• 15. -5( -M 6)
• 16. Y(Y Z)
• 17. 12 16
• 18. -8(6 - C)
• 19. (4 - T)(-7)
• 20. 2(3 - 6)

• 1. 5 ( 4 - 3)
• 2. (2X 5) 7
• 3. 2(7 - 3D)
• 4. (6M 1) 3
• 5. -3 ( 5T - 2)
• 6. 3 ( T - 5)
• 7. 3H(H - 2)
• 8. 2 ( Y - 2 Z)
• 9. -5 ( 6 3M)
• 10. (Y - 6 )(-2)