# The Distributive Property of Algebraic Expressions Essay

Janet Mency

MAT 221

Instructor: Amy Glidewell

January 25, 2014

Completing algebra problems can be difficult if you don’t understand the properties of real numbers. There are several properties in algebra dealing with both integers and real numbers; one that will be the focus of this report will be the distributive property. We use this property when we are combining addition and multiplication in an algebraic expression. Let’s say that you are presented with the expression 6x(2 + y) = 9x + 5xy, now with this problem the order of operation would have you to add the terms in parenthesis first, by using the distributive property it allows to simplify the problem by multiplying all

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2a(a-5) + 4(a-5) The algebraic expression that will be simplified.

2a^2-10+4a-20 The distributive property removes the parentheses.

2a^2+4a-10-20 The next stage is to combine the like terms by adding 2a^2 + 4a - 30 coefficients. As you see in the problem we arrange the like terms together in order by using commutative property to complete the expression. That’s the property where we can rearrange the numbers where we want them. The next example will be a little more challenging because you have move variable in the expression.

2w-3+3(w-4)-5(w-6) The algebraic expression that will be simplified.

2w-3+3w-12-5w+30 The distributive property removes the parentheses.

2w+3w-5w-12+30 Combine the like terms by adding coefficients.

18 Once the like terms are added then the expression is simplified. Because 2w + 3w – 5w give you 0 then the answer would be 18, it kind of like it 0 out. My final expression that demonstrates the use of distributive property will be using decimals. Even though it uses decimals the concept is the same.