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Distributive Property - Simplify or Factor Expressions

by Dawn
(Sebring, Ohio)










































Distributive Property

The Distributive Property is one of the seven basic number properties: Associative, Commutative, Distributive, Identity, Inverse, Closure, and Density.

     • What is the Distributive property?

     • When is the Distributive property used?

     • Explain and demonstrate how to use the Distributive property with an example containing at least one variable.



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Sep 05, 2012
Distributive Property
by: Staff


Answer:

Part I


What is the Distributive property?

     The Distributive Property is one of the seven basic number properties: Associative, Commutative, Distributive, Identity, Inverse, Closure, and Density.


     The Distributive Property allows you to simplify an expression containing parentheses to an expression without parentheses.

       For example, using the Distributive Property:

            x(y + z) = xy + xz

            3(4 + 2) = 3*4 + 3*2

     The Distributive Property is formally defined as "the distribution of multiplication over addition" because it combines the following two operations: multiplication and addition .

         There is only one Distributive Property. There is not a separate Distributive Property for addition, and another Distributive Property for multiplication.


When is the Distributive property used?


     1. The Distributive Property is used to simplify an expression, an equation, or arithmetic which contains a parentheses multiplied by something else:

         i. parentheses multiplied by a constant

                  3(a + b) = 3a + 3b

                  y = 3(a + b) = 3a + 3b

                  3(20 + 5) = 3*20 + 3*5

         ii. parentheses multiplied by a variable

                  x(a + b) = ax + bx

                  f(x) = x(a + b) = ax + bx

                  x(20 + 5) = 20x + 5x

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Sep 05, 2012
Distributive Property
by: Staff


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Part II

         iii. parentheses multiplied by another parentheses

                  (x + y)(a + b) = ax + bx + ay + by

                  f(x,y) = (x + y)(a + b) = ax + bx + ay + by

                  (40 + 3)(20 + 5) = 40*20 + 40*5 + 3*20 + 3*5


     2. The Distributive Property is used to factor an expression, an equation, or number:

         i. terms multiplied by a constant

                  3a + 3b = 3(a + b)

                  y = 3a + 3b = 3(a + b)

                  43*25 = (40 + 3)(20 + 5)

         ii. terms multiplied by a variable

                  ax + bx = x(a + b)

                  f(x) = ax + bx = x(a + b)

                  ax + bx + ay + by = (x + y)(a + b)

                  f(x,y) = ax + bx + ay + by = (x + y)(a + b)


                  20x + 5x = x(20 + 5)

         iii. terms with exponents

                  f(x,y) = x² + 8x + 15 = (x + 3)(x + 5)


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Sep 05, 2012
Distributive Property
by: Staff


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Part III


Explain and demonstrate how to use the Distributive property with an example containing at least one variable.

         i. parentheses multiplied by a constant

                  3(a + b) = 3*a + 3*b = 3a + 3b

                  y = 3(a + b) = 3*a + 3*b = 3a + 3b

                  3(20 + 5) = 3*20 + 3*5 = 60 + 15

         ii. parentheses multiplied by a variable

                  x(a + b) = x*a + x*b = ax + bx

                  f(x) = x(a + b) = x*a + x*b = ax + bx

                  x(20 + 5) = x*20 + x*5 = 20x + 5x

         iii. parentheses multiplied by other parentheses

                  (x + y)(a + b) = x*a + x*b + y*a + y*b = ax + bx + ay + by

x + y
a + b
x*a + x*b + y*a + y*b

= ax + bx + ay + by


                  f(x,y) = (x + y)(a + b) = x*a + x*b + y*a + y*b = x*a + x*b + y*a + y*b = ax + bx + ay + by

                  (40 + 3)(20 + 5) = 40*20 + 40*5 + 3*20 + 3*5 = 800 + 200 + 60 + 15

                  f(x,y) = (x + 3)(x + 5) = x² + 8x + 15

x + 3
x + 5
x*x + x*3 + 5*x + 5*3

= x² + 3x + 5x + 15

= x² + 8x + 15






Thanks for writing.

Staff
www.solving-math-problems.com



Sep 06, 2012
Distributive property
by: Anonymous

Thank You so very much

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