Distributive Property
Kimberly Smith
MAT 221 Introductions to Algebra
Instructor: Andrew Halverson
February 15,2014

I will be using distributive property to solve how properties of real numbers are used while I simplified the three given expression. To solve these three math problem I will use the distributive property to remove the parentheses in the problem. I will also combine like terms by adding coefficients and add or subtract when needed. Finally I would have my answer and then decide if the answer is simplified, if not I will simplify. The solving of properties of real number the properties of real numbers are important to know in all subjects, even complex numbers, because many of the properties are shared. Additionally the argument to any equation in algebra is real; therefore, algebraic expressions only manipulate reals (that is, if you have integer coefficients and no radicals).

1. 2a(a-5)+4(a-5) = The given expression
2a^2-10a+4a-20 = I will use the distributive property to remove parentheses so I can combine like terms by adding coefficient. 2a^2-6a-20 = Is simplified no combine like terms by adding coefficients 2a^2-6a-20 = Answer

2. 2w – 3 + 3(w – 4) – 5(w – 6)= The given expression
2w - 3 + 3(w - 4) - 5(w - 6) = Distributive property removes parentheses
2w - 3 + 3w - 12 - 5w + 30 = Combine like terms
2w + 3w - 5w - 3 -12 + 30 = Combine like terms by adding coefficients and add and subtract to get sum. Use the commutative property to switch places.
5w - 5w - 15 + 30= Combine like terms subtract two of variable terms are combine and two of constant terms are combine
0w+15= 15 =Constant
= 15

3. 05(0.3m+35n)-0.8(-0.09n-22m) the given expression
.15m+1.75n+.072n+17.6m = the distributive property removes the parentheses
-.8(-09n-22) = .072n+17.6m= Expand remembering minus = plus = 0.015m + 1.75n + 0.072n + 17.6m = Group like terms using the Commutative property = 17.615m + 1.822n = like terms are added by coefficients

I used the distributive property to solve how properties of real numbers are used while I simplified the three given expression. I solved these three math problem I will use the distributive property to remove the parentheses in the problem. I will also combine like terms by adding coefficients and add or subtract when needed. Finally I would have my answer and then decide if the answer is simplified, if not I will have to simplify. The conclusion of solving properties of real number the properties of real numbers are important to know in all subjects, even complex numbers, because many of the properties are shared. For example, the zero property tells us in algebra what the zeroes of a function are. The distributive property allows us to perform operations like: first, outer, inner, and last (FOIL) method and factoring. Additionally the argument to any equation in algebra is real; therefore, algebraic expressions only manipulate reals (that is, if you have integer coefficients and no radicals).