The Distributive Property

1
The Distributive Property

• A. Use the distributive property.
• 1.) Distributive property
• a(b c) ab ac a(b - c) ab -
  ac
• (b c)a ba ca (b - c)a ba
  ca

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a.) Using an Area Model

• Find the area of a rectangle whose width is 5 and
  whose length is x 3.
• You can find the area in two ways.
• Area of One Rectangle 5( x 3 ) or
• Area of Two Rectangles 5(x) 5(3)
• Both ways produce the same area, the following
  statement is true. 5( x
  3 ) 5(x) 5(3)

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b.) Using the Distributive Property

• 8(x 9)
• 8 ( x ) 8 ( 9 ) Distribute the
  8.
• 8x 72 Simplify.
• -5(x - 6)
• -5 ( x ) - ( -5 )( 6 ) Distribute
  the 5.
• -5x - (30) Simplify.
• -5x 30

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B. Simplify expressions by combining like
terms.

• 2.)Coefficient In a term that is the product
  of a number and a variable, the number is the
  coefficient of the variable.
• 3.)Like terms Like terms are terms in an
  expression that have the same variable raised to
  the same power.
• 4.)Constant terms Constant terms are terms
  with no variable factors
• 5.) Simplified An expression is simplified if
  it has no symbols of grouping and if all the like
  terms have been combined.

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c.) Combining like terms

• 10x 13x Use the distributive property.
• ( 10 13 )x Add coefficients.
• 23x

b. 2xy - 5 8xy 3 Rewrite as an
addition expression 2xy
(-5) 8xy 3. 2xy 8xy (-5) 3
Group like terms. 10xy - 2
Combine like terms.
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Use the distributive property to rewrite the
expression without parentheses.

1. 6(x 5)

• (y 7)8

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Simplify the expression by combining like terms.

• -5x 2x
• -10x - 8x

• 22m (- 4m)
• -32 t 18

8
Apply the distributive property. Then simplify by
combining like terms.

1. 2(3x 1) x

1. -2(3a -5) 2a

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Geometry

• Write an expression for theperimeter of the
  triangle shown below.

2x 2x 3x - 5