Mat 221 Introduction to Algebra
Instructor Jason Hazel
September 6, 2014
Simplifying Expressions We will be simplifying mathematical expressions. Simplifying an expression means to bring the math expression to the simplest terms, by using the order of operation commonly known as PEMDAS. The terms we will simplify in this paper will be 2a (a-5) +4(a-5), 2w-3+3(w-4)-5(w-6) and 0.05(0.3m+35n)-0.8(-0.09n-22m). PEMDAS stands for parentheses, exponents, multiplication, division, addition and subtraction. We use the operation in this order. First remove and parentheses multiply any exponents then apply multiplication, division addition or subtraction. This is a good way to eliminate confusing while solving a mathematical expression. For the first expression we will simplify 2a (a-5) +4 (a-5). We will first use distributive property by multiplying each term inside side the parentheses by the 2a. 2a*a equals 2a², the 2 squared is a coefficient, meaning that it will be multiplied by its self. So now we have 2a²*10a+4(a-5). We will do the same on the other side by distributing 4 to everything in the parentheses. Our expression will now as 2a²-10a+4a-20, you notice that all the parentheses are gone. Next we will combined all like terms, since 4a and -10a are alike, we will subtract, leaving us with -6a. Our simplified expression will now read 2a²-6a-20. The next expression is 2w-3+3(w-4)-5(w-6). This expression is a little longer, but all the steps from the first example apply. First we will get rid of the first set of parentheses, by multiplying 3*w and 3*-4, giving us the expression 2w-3+3w-12-5(w-6). To remove the remaining parentheses, we will do the same thing with -5. Multiplying -5*w and -5*6, changes our expression once again to 2w-3+3w-12-5w+30. We will now re organize our polynomials from the highest to the lowest. 2w-3+3w-12+30-5w, is what we will work with now. As with the first example, we will combine like terms, 2w+ 3w will give us 5w. -5w and 5w are like terms, when we add them we get 0. The expression now reads, 0-3-12+30 subtract 12 from -3 to get -15. And the following expression remains -15+30, leaving us with the simplified expression of 15. The final
