Understanding the properties of algebra is important in learning how to simplify algebra expressions. When simplifying and solving algebra problems, or as it is called, simplifying expressions, one must be able to understand the distributive property. The distributive property, sometimes called distribution, is used to apply multiplication across two or more terms inside of parentheses and results in the removal of the parentheses. The removal of the parentheses via the distributive property makes the algebra expression more simplified. The number preceding the variables in a term is called the coefficient (Dugopolski, M. (2012).
The commutative property allows movement of terms to different locations within expressions and the operation symbol in front of the term will move as well. The associative property is used to group like terms together so they can all be combined. Like terms must have the same variable raised to the same power, or with the same exponent.
While simplifying the following expressions, the properties of real numbers will be used and identified. The math work will be aligned on the left while the discussion of properties is on the right side of each line.
A) 2a (a + -5) +4(a + -5) The given expression 2a^2 – 10a + 4a -20 The distributive property removes the parentheses 2a^2 – 6a – 20 Like terms are combined by adding coefficients. This expression is now fully simplified because nothing else can be computed. In this example it was not necessary to change the order of any of the terms because the like terms were already together in the middle of the expression in step 2. B) 2w – 3 +3(w – 4) -5(w – 6) The given expression
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2w – 3 + 3w -12 -5w + 30 The Distributive properties removes the parentheses. 2w + 3w – 5w – 12 + 30 Like terms are arranged together using the communicative property to switch places. 2w, 3w, and -5w are like variable terms while -3, -12, and 30 are like constant terms. These can all be added or subtracted. 5w – 5w – 9 + 3 Two of the variable terms are added and two of the constant terms are also added. -9 + 3 The remaining pairs of like
terms are added.
-6 This expression is now fully simplified.
C) 0.05(0.3m + 35n) – 0.8(-0.09n – 22m) The given expression 0.015m + 1.75n + 0.072n + 17.6 The distributive property removes the parentheses. 0.015m + 17.6m + 1.75n + 0.072n Like terms are arranged together using the commutative property. All terms are variable terms but only those with the same variable may be combined. 17.615m + 1.822 Like terms are combined by adding coefficients. This one only looked more complicated because of the decimal numbers, which require the decimals lined up to add or subtract. The basic steps are not any different from the other examples.
As can be seen in the example of the algebra problems above, simplifying algebra expressions in order to make them easier to process is not as “simple” as it would seem. First, the distributive property has to be utilized in order to remove the parenthesis. Then, like terms are organized adding the coefficients. . The remaining numbers are then simplified into their smallest forms to complete the act of simplifying the algebra expression. With some practice, one can get the hang of how to simplify and do so with little ease in time.
