# Mat221 - Week 1 Assignment

Student

MAT 221 – Introduction to Algebra

Instructor

August 18, 2013

Algebra is a branch of Mathematics that we use in everyday life without realizing it. When we fill up with gas we will quite often do that quick calculation on how many miles be gallon we got. We might use it to determine how many apples could be in a pound after weighing just one of average size. Many such applications of algebra like this are done every day. Algebra is like doing regular math but using non- numeric math objects instead. It can also be thought of as a kind of language that uses its own vocabulary. Some consider algebra to be like puzzles. You could start with something like “a – 2 = 5” and what you will end up with is the answer to the puzzle of what the variable of a is. In this case a is 7. There are many properties of Algebra. Distributive, associative, identity, inverse, closure, simplification and commutative are a few we studied in this week’s assignments. Below I will show a few examples of Algebra simplifying some expressions using the distribution properties with like terms and coefficients. 2a (a – 5) + 4(a – 5) we were given this expression to simplify.

Simplifying this expression will first involve using the distribution property to remove the parenthesis

2a *a + 2a * -5 + 4 * a + 4 *-5 Now we will take our new expression and combine like terms by adding the coefficients 2a^2 +6a -20We now have the original expression show in simplest terms. The ‘^’ symbol is being used to show the exponent for the variable a.

2w – 3 + 3(w – 4) – 5(w – 6) We were given this expression to simplify.

2w – 3 + 3w – 12 – 5w + 30 our first step to simplify is to remove the parenthesis and do the multiplication.

2w + 3w – 5 w – 3 – 12 + 30 Now we will need to take...

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