Simplifying Expressions
Simplifying Expressions
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
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.
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
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.