# Simplify the Following Algebraic Expressions

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### Question Description

Simplifying Expressions

Read the following instructions in order to complete this assignment and review the example  (ATTACHED) of how to complete the math required for this assignment:

• Use the properties of real numbers to simplify the following expressions:

• 2a(a – 5) + 4(a – 5)
• 2w – 3 + 3(w – 4) – 5(w – 6)
• 0.05(0.3m + 35n) – 0.8(-0.09n – 22m)
• Write a two- to three-page paper that is formatted in APA style and according to the Math Writing Guide. Format your math work as shown in the Instructor Guidance and be concise in your reasoning. In the body of your essay, do the following:

• Demonstrate your solution to the above problems, making sure to include all mathematical work. Show every step of the process of simplifying and identify which property of real numbers was used in each step of your work. Please include your math work on the left and the properties used on the right.
• Explain why the properties of real numbers are important to know when working with algebra. In what ways are they useful for simplifying algebraic expressions?
• Incorporate the following five math vocabulary words into the text of your paper. Use bold font to emphasize the words in your writing (Do not write definitions for the words; use them appropriately in sentences describing your math work):

• Simplify
• Like terms
• Coefficient
• Distributive
• Removing parentheses
MAT221.W1.AssignmentExample.pdf

Running Head: SIMPLIFYING EXPRESSIONS Running head should use a shortened version of the title if the title is long! All capital letters for the title and the words Running and Head should be capitalized as well. Simplifying Expressions (full title; centered horizontally & vertically) First Name Last Name MAT 221 Dr. XXXXXXX XXXXXXXX Date 1 SIMPLIFYING ALGEBRAIC EXPRESSIONS 2 Simplifying Expressions Be sure to have a centered title on page 1 of your papers. [The introductory paragraph must be written by each individual student and the content will vary depending on what the student decides to focus on in the general information of the topic. YOUR INTRODUCTION SHOULD CONNECT MATH CONCEPTS AND REAL-WORLD APPLICATIONS. DO NOT INCLUDE THE DIRECTIONS IN THE INTRO! The following paragraph is not an introduction to the paper but rather the discussion called for in part 2 of the instructions.] The properties of algebra are important to know and understand how they work because in simplifying and solving methods one must be able to properly move terms around and put expressions and equations into the simplest form possible. 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 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. [Notice that these expressions are not the same as in the assignment, although they are similar enough to demonstrate everything needed in the actual assignment.] A) 3a(a – 7) + 6(a –7) The given expression 3a2 – 21a + 6a – 42 The distributive property removes the parentheses. 3a2 – 15a – 42 Like terms are combined by adding coefficients. SIMPLIFYING ALGEBRAIC EXPRESSIONS 3 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) 5w – 7 + 7(w – 3) – 4(w – 9) The given expression 5w – 7 + 7w – 21 – 4w + 36 Distributive property removes the parentheses. 5w + 7w – 4w – 7 – 21 + 36 Like terms are arranged together using the commutative property to switch places. 5w, 7w, and -4w are like variable terms while -7, -21, and 36 are like constant terms. These can all be added or subtracted. 12w – 4w – 28 + 36 Two of the variable terms are added and two of the constant terms are also added. 8w + 8 The remaining pairs of like terms are added. This expression is now fully simplified because 8w and 8 cannot be added. C) 0.03(0.7m + 24n) – 0.9(-0.06n – 18m) 0.021m + 0.72n + 0.054n + 16.2m The given expression The distributive property removes the parentheses. 0.021m + 16.2m + 0.72n + 0.054n Like terms are arranged together using the commutative property. All terms are variable terms but only those with the same variable may be combined. SIMPLIFYING ALGEBRAIC EXPRESSIONS 16.221m + 0.774n 4 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. [The conclusion paragraph must be written by each individual student and the content will vary depending on what the student decides to include in their summary. DO NOT INCLUDE PERSONAL NARRATIVE LIKE “I LEARNED…” OR “WE CAN DO….”. BE SURE TO SUMMARIZE WHY THE CONCEPT(S) ARE IMPORTANT AND HOW THEY CAN BE CONNECTED TO OTHER CONCEPTS.] SIMPLIFYING ALGEBRAIC EXPRESSIONS Reference Dugopolski, M. (2012). Elementary and intermediate algebra (4th ed.). New York, NY: McGraw-Hill Publishing. Use the word ‘Reference’ or ‘References’ as the title. THERE IS NO COLON OR UNDERLINE. Textbook should ALWAYS be included in every assignment! Be sure to use appropriate indentation (hanging), font (Arial or Times New Roman), and size (12). 5

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