Simplifying Expressions
Simplifying Expression
MAT 221 Alicia Davis
March 8, 2014
When solving algebraic equations, there are many properties that need to be identified to solve the equation. Some of the properties to be identified are distributive which helps remove the parentheses, and then to simplify you must combine like terms. Another term you need to identify is coefficients, which is for example in an equation could be 4a in 4a+7=12. To solve equations you must be able to identify all of the properties and know the steps that go along with them. In an equation, distributive property is used to remove parentheses around two or more terms. To accomplish this one must multiply through two or more terms with in the parentheses, in result removing the parentheses. Next you must simplify by combining like terms. To combine like terms, one must use commutative property to arrange like terms to be all together in the equation. Then you must add the coefficients. While simplifying the following expressions, we will show examples of how the properties of real numbers will be used and identified.
A.) 2a(a-5)+4(a-5) The initial equation.
2a2 -10a+4a-20 Distributive removes the parentheses.
2a 2-6a-20 By adding coefficients, like terms are combined.
B.) 2w-3+3(w-4)-5(w-6) The initial equation.
2w-3+3w-12-5w+30 Distributive properties remove the parentheses.
2w+3w-5w-3-12+30 Using commutative property, arrange the like terms together to add, put 2w, 3w, and 5w together and then 3, -12, and 30 together to combine.
5w-5w-15+30 two variable terms are added and two constant terms are added.
0w+15 The two pairs of like terms remaining are combined to simplify the answer.
15 The problem solved in simplest form.
C.) 0.05(0.3m+35n)-0.8(0.09n-22m) The initial equation. 0.015m+1.75n-0.072n+17.6m Distributive property removes the parentheses 0.015m+17.6m+1.75n-0.072n Like terms are arranged together by commutative property. All
MAT 221 Alicia Davis
March 8, 2014
When solving algebraic equations, there are many properties that need to be identified to solve the equation. Some of the properties to be identified are distributive which helps remove the parentheses, and then to simplify you must combine like terms. Another term you need to identify is coefficients, which is for example in an equation could be 4a in 4a+7=12. To solve equations you must be able to identify all of the properties and know the steps that go along with them. In an equation, distributive property is used to remove parentheses around two or more terms. To accomplish this one must multiply through two or more terms with in the parentheses, in result removing the parentheses. Next you must simplify by combining like terms. To combine like terms, one must use commutative property to arrange like terms to be all together in the equation. Then you must add the coefficients. While simplifying the following expressions, we will show examples of how the properties of real numbers will be used and identified.
A.) 2a(a-5)+4(a-5) The initial equation.
2a2 -10a+4a-20 Distributive removes the parentheses.
2a 2-6a-20 By adding coefficients, like terms are combined.
B.) 2w-3+3(w-4)-5(w-6) The initial equation.
2w-3+3w-12-5w+30 Distributive properties remove the parentheses.
2w+3w-5w-3-12+30 Using commutative property, arrange the like terms together to add, put 2w, 3w, and 5w together and then 3, -12, and 30 together to combine.
5w-5w-15+30 two variable terms are added and two constant terms are added.
0w+15 The two pairs of like terms remaining are combined to simplify the answer.
15 The problem solved in simplest form.
C.) 0.05(0.3m+35n)-0.8(0.09n-22m) The initial equation. 0.015m+1.75n-0.072n+17.6m Distributive property removes the parentheses 0.015m+17.6m+1.75n-0.072n Like terms are arranged together by commutative property. All