### Algebraic expressions

## Introduction

In the introduction to Algebra, the first assignment for the first week will involve using real numbers in place of integers to simplify expressions. Everyone needs to take his/her time to grasp the rules and the steps which are followed in algebra as this will form a concrete base for the algebraic expression understanding. One needs to understand the mathematical fundamental elements so as not to incur problems in solving any algebraic problems. For instance, one needs to be clear with the properties of integers as these are the same properties which apply to the real numbers. The first step in dealing with equations is removing the parenthesis. If an equation requires you remove the parenthesis from the equation, distribution becomes a necessity. Like terms should be grouped together when multiplying the integers that are inside the parenthesis to perform any indicated operation (Dugopolski, M.(2012 ), 2, p.67).

The following is how I attempted to handle the assigned equations in the simplest form. In the left side of the page, I have put the mathematic equation, and in the right side there is my explanation of the steps I followed.

2a(a-5)+4(a-5) Equation

=2a²-10a+4a-20 remove the distributive properties from the parenthesis

= 2a² -6a-20 then we get the coefficient.

=a²- 3a – 10 then we simplify the expression.

In the next equation,

2. 2w-3+3(w-4)-5(w-6) the equation

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=2w-3+3w-12-5w+30 remove the distributive properties from the parenthesis

=2w+3w-5w-3-12+30 then we get the coefficients and.

=15 combine them

In the third equation,

3. 0.05(0.3m+35n)-0.8(-0.09n-22m) the equation

=0.015m+1.75n+0.072n+17.6m remove the distributive property from the parenthesis

=0.015m+17.6m+1.75n+0.072n simplify by putting the like terms together and

=17.615m+1.822n combine them

#### References

Dugopolski, M. (2012 ).

Elementary and Intermediate Algebra. New York, NY: McGraw-Hill.