Transcript:

How to simplify expressions using the order of operations? I'm Bon Crowder with MathFour.com, and we're going to talk about simplifying this expression using the order of operations. The first thing to note is what the order of operations are. Usually we remember them as PEMDAS, or Please Excuse My Dear Aunt Sally. Which represents, parenthesis, exponents, multiplication, division, addition and subtraction. There's a couple glitches on this, though. Parenthesis also means isolation. Anything in brackets, underneath a square root sign, anything isolated in the top or bottom of a fraction. All qualify as parenthesis. Exponents also includes roots. So, multiplication and division go together, addition and subtraction go together. So, let's look at this guy. First we see, we have some isolation. So, I'm going to put parenthesis around these guys that are isolated. And then, I notice, gee, within the parenthesis or isolation, I can't do anything. Before X minus one, they just won't go together. So, I have to do other things, namely that square comes next, it's part of the exponents, roots piece. So, I need to square this and I do what squaring means, is two copies of that. And then, I'm just going to copy this down to carry it with me. So, I'm going to square these or square this one by multiplying them. So, I multiply both of those and then, I multiply both of those. That's an extended distributive property. So, I have three and this is in a bundle, 16-X squared minus four-X, minus another four-X plus one. And then, I still have this six-X plus eight divided by two. Within the parenthesis or the isolation, now I still can actually do something. So, I have 16-X squared minus eight-X, because those go together as like terms, plus one. And then, I still have my six-X plus eight over two. Now, I can attack either of these next. I'm going to just go for the front. This three then can be distributed to all the pieces. So, I have three times 16, is 30 plus 18 is 48-X squared. Three times eight is 24, that's X and three times one is three. Now, I'm forced to deal with this fraction hanging off the end. What this over two means in the fraction, is it's one-half of this. So, again I'm just going to copy what I have, don't forget to plus in there, it's really easy to do. Now, I'm going to distribute the one-half to both pieces. So, I have 48-X squared, don't loose the eight, minus 24-X plus three. Plus one-half of six, is three-X, one-half of eight is four. Now, I'm ready to combine like terms. So, let's see, how about some green. 48-X squared, nobody matches him. 24-X, negative 24-X and three-X match, so that's minus 21-X. And then, I have a three and a four that match. And there I have simplified an expression using the order of operations. I'm Bon Crowder with MathFour.com, enjoy.