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The Distributive Property

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. a.) Using an Area Model.

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The Distributive Property

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  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

  2. 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)

  3. 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

  4. 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.)SimplifiedAn expression is simplified if it has no symbols of grouping and if all the like terms have been combined.

  5. 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.

  6. 6(x + 5) (y – 7)8 Use the distributive property to rewrite the expression without parentheses.

  7. -5x + 2x -10x - 8x 22m + (- 4m) -32 + t + 18 Simplify the expression by combining like terms.

  8. 2(3x + 1) + x -2(3a -5) + 2a Apply the distributive property. Then simplify by combining like terms.

  9. Geometry • Write an expression for theperimeter of the triangle shown below. 2x 2x 3x - 5

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