# 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.

### Comments for Distributive Property - Simplify or Factor Expressions

 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 --------------------------------------------

 Sep 05, 2012 Distributive Property by: Staff -------------------------------------------- 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) --------------------------------------------

 Sep 05, 2012 Distributive Property by: Staff -------------------------------------------- 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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