Simplifying Algebraic Expressions

Simplifying Algebraic Expressions

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MAT 221

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Simplifying Algebraic Expressions

The simplifying of expressions is necessary when using Algebra. Turning cluttered numbers and symbols into easier to read equations is very necessary. We must both know how the process works and why it works. In this assignment, I will do my best to simplify the given expressions and outline the process.

1. 2a(a – 5) + 4(a – 5) Given Expression

2a²-10a+4a-20 Distribution due to distributive property removes parentheses

2a²-6a-20 combining like terms lets us simplify the expression

The expression is now in the simplest form

1. 2w–3+3(w–4)–5(w–6) Given Expression

2w-3+3w-12-5w+30 Distribution due to distributive property removes parentheses

2w+3w-5w-3-12+30 Like terms are arranged together using commutative property

0+15 Like terms are combined by adding coefficients

15 Final simplified answer

1. 0.05(0.3m + 35n) – 0.8(-0.09n – 22m) Given Expression

0.015m + 1.75n + .072n + 17.6m Distribution property lets us simplify expression

0.015m + 17.6m + 1.75n +.072n Commutative property groups like terms

17.615m + 1.822n Final simplified answer due to not being able to further simplify the two given coefficients and variables

Simplifying algebraic expressions is much easier when using the properties of real numbers. The distributive property seems to be the most useful by allowing an expression to be simplified by using multiplication and addition.

Reference

Dugopolski, M. (2012). Elementary and intermediate algebra (4th ed.). New York, NY: McGraw-Hill Publishing.