 There's the magic sound so we're live listen to prep your paper polynomial review, and I think I said to you normally I Have the workbook notes will use those this is just some quick review to brush the cobwebs off again I'm going to assume we're at the lowest common denominator. I'm going to assume you've forgotten everything With the understanding probably most of you haven't and that means this lesson can go pretty quick. I hope I think oh So once again We're going to jump right into this the instructions are just going to say simplify Simplify is one of those math words that means a lot of things to me What it means is get rid of brackets tidy it up and write it as short as possible Simplify are you new to my class? I forgot to do attendance hang on here silly me pause Here we go Simplify I expect you've been doing this since grade 9 Multiplying polynomials and gathering like terms so in your homework. You're going to have some stuff like oh Or how about this? Example one give me a pen example 6a squared bracket a squared plus 3a Minus 9 What did we call this if you had mr.. Raqqa you called it? Front door bomber or something. Anyways get rid of brackets distribute whatever phrase works for you However, you want to remember it. I'm totally good with that. I think I told you I almost always take the one second to do that because it gets rid of most of my silly mistakes 6a squared times a squared. What is 6a squared times a squared? well when we're multiplying Letters and variables. It's multiply numbers by numbers. What's the number in front here? It's invisible visible one so six times one six What's a squared times a squared? eight of the fourth What's six times positive three? sorry, and I say to myself Positive 18 reminds me to put a plus sign there and what's a squared times a? a cubed and That's a nine not an a let me make that a little more obvious by going like that So it sort of looks like a nine now looks like a jeep shut up 6a squared times negative nine numbers times numbers six times negative nine. I'm pretty sure is negative 36 and The a squared That's what I said. Can't you read my writing is my writing that bad? I should be able to get that and Then the last thing once you've done getting rid of brackets double check Are there any like terms in my answer that I can gather? No, I can't add a fourths to a cubes to a squared You guys handle that faster than I plan. Let's pick up the pace a little bit Example to five x squared y cubed times negative three x y squared minus Four x squared y squared z plus six x squared y squared I think out of all the mathematical operations Emily if you know your times tables Multiplying is the easiest of the mathematical operations because it's much more straight memorizing anything else I make far more sloppy mistakes when I'm adding and subtracting than when I'm multiplying so here We have multiplying some polynomials again. It's going to be that I Think I told you last day if I ever draw a Zed by the way, I'll put a line through it So, you know, it's not a tube Because my writing is that bad and don't want to talk me through this Sure Marcus you switched numbers by numbers So five times negative three is I Totally agree with that x squared times x is Y cubed times y squared is Done move on to the next term. Keep going five times negative four Negative 20 and I say that in my mind to remember put the negative there the minus sign x squared times x squared x to the fourth Y cube times y squared Y to the fifth No Zeds times one Z. I think just a single solitary Z last one positive five times positive six Positive 30 x squared times x squared x to the fourth Y cubed times y squared y to the fifth Double check are there like terms anywhere? I thought these were like no this has got a Zed this doesn't so I think that's as Simplified as it'll get a few more we're done That was where you started in grade nine when you learned the Distribution principle front door bomber when you learn that if you have terms in the brackets and a number in front It's multiplying everything inside the brackets Then they Kick things up a notch Something like this They still have something in brackets But in front they put two things Instead of one thing in front of the brackets, it's two things in front of the brackets and The rule is still the same Sierra Sorry, it's trying to come up with names The rule is still the same. It's still everything in front times everything in the back Although I think they give you an acronym to help you remember so you don't miss anything we call it call it call it foil okay, and That's become so ubiquitous that we often just refer to everything as foil even though technically foil is only two terms times two terms I Again just do this. I had a teacher though who used to do it this way Don't write this down, but it was a good way to remember he would go like that like that Like that and like that and you'd put a little eye right there a little eye right there There's your happy face and he would say let George do it was always his acronym He would taught us in grade eight to draw the little happy face. I guess I should put the eyes there there There's the happy face It's still foil Whatever way you want to do it. It's everything in the front times everything in the back However in your prime Some of you in grade nine and ten Might have been able to do these in your head showing no work go ahead this first one. I am gonna show all my work Three x times two x is six x squared Three x times positive four. I got a disagree 12 x negative five times two x negative 10 x negative five times positive four Negative 20 and then you have like terms together Six x squared. I have a 12 x minus a 10 x. I'm pretty sure that's a positive 2x Minus 20 try one more If you want to do it in your head go ahead example for 2x plus 7 5x minus 1 am I right? I did it all in my head. I could be wrong They will check people looking funny. Am I right? Everything in the front times everything in the back gather like turns How many you got that? Been doing that since grade nine The one they introduce in grade ten is this hopefully Two more and I'm nearly done in grade ten So grade nine they go two terms times two terms in grade ten they go two terms times Three terms two x plus seven in brackets and then three x squared plus four x Plus five in brackets and you can call this foil if you want to it's I mean the acronym doesn't work Here's what I remember. It's very simple Sam. I just remember everything in the front times everything in the back And I go systematically I go the first term Times all three and Then because it gets crowded because the last term times all three But I draw these loops underneath just so it's not so crowded just me you don't have to do with that Way, but over the years so you're ready. I'm gonna go real systematic I'm gonna get rid of the loops and draw them as I go so I can make sure I catch them all It's gonna be first terms times first term Sam. What is 2x times 3x squared? I Totally agree and then it's gonna be first times second. What is 2x times 4x? I Totally agree What is 2x times positive 5? yet again, I totally agree and then Keep going kiddo seven times 3x squared I Agree are there like terms we can gather Okay Again, I'm not sure how much your teacher taught you to write when you're gathering like terms Some teachers prefer the kids to rewrite everything in order. I've already told you my goal this year is Intelligent safe, but lazy at the same time so Danielle if I was gathering like terms I would say let's start with the biggest exponent. Are there any other x cubes anywhere? I would write it and Then I cross it out just to let myself know I took care of those Then I'll do all the x squareds. I have a positive 8x squared. I have a positive 21x squared Danielle What is 8x squared plus 21x squared and I would cross those out to remind myself that I'd taken care of those ones This is how this is how I make sure I don't this end right Danielle keep going. What's 10x and 28x? Yep Are you doing the math in your head? Good. Yeah, sure And I got one term left it drops down like a domino Boston is every term crossed out. That's my built-in. Hey, I don't think I missed anything If they get longer especially then I get more systematic We used to in the old curriculum do three terms times three terms Trinomial times trinomial, then you really had to be organized, but I still didn't want to write 20 lines I want to see if I could still do it to maybe three lines. So that's kind of our goal Okay, how many got that okay? That's the lesson really quick review of algebra. So What's your homework? Oh They're like they're bad. They're terrible first of all, do you have the equation solving review number three you can still work on that one