[Music] welcome back to yay math org with yay math in studio I'm Robert of dudes with my good friend Zach behind camera and today we're going to be talking about operations with polynomials this stuff is a little weird if you don't know what's going on but the second you see it it's just gonna click right into place and that's my hope for you that when you see it it's just gonna make sense so let's just jump right in the first I guess concept that this section tries to teach in the books is this concept of degree alright so degree basically is the highest value of the exponent that's all that is so if you have something like X to the fourth that's degree four in this case we look through this entire polynomial we're not multiplying anything we're only subtracting so this would be a degree two over here sometimes you have situations like this and then you're on a fourth this would be degree seven actually when you multiply these two terms even though they don't combine the power of the exponents culminate in the power of seven so this will be degree seventh this would be degree four once you understand degree just keeping in the back of your mind for future problems which we're gonna do in the other videos okay let's learn how to conquer this particular polynomial in which they have us subtract these two so pretty much when we're adding or subtracting or combining like terms the important thing to keep in mind is it's sort of like we're subtracting this whole thing which means negative one distributes to all three terms in other words all three signs will change inside it's called distributing the negative so let's go ahead and do that this would results in negative x squared plus 2x minus 10 and then over here we realized that the parentheses serve no purpose so we can just take them off 3x squared plus 2 X minus 7 and combine those up like terminologies combining like terms just go through it 3x squared and minus x squared results in 2x squared 2x plus 2x is 4x negative sin you have a 7 negative 7 and negative 10 not negative sin negative zebb to be like everything not negatives n negative 7 and negative 10 we minus 17 pretty much it distribute the negative through other problems we'll have a plus here no problem you just add all the like terms ok not everyone would be so not every problems so friendly sometimes they have as multiplying polynomials we're gonna do that now so 2x minus y cubed oh the temptation to just bring in the cube to 2x and negative Y oh people love it I'm gonna put a big fat non equal to here people think it's 2x times 2x times 2x which would be 8x cubed negative Y times negative Y times negative Y it would be minus y cubed and it's wha-wha doesn't work that way we have to multiply these binomials together so to visualize that we have to write them side by side I'm going to start with two of them two out of the three okay let's take this take this off no wah wah vibes no what wives no all our lives 2x minus y 2x the - why people call this foil first outer inner last basically it's distributive property the 2x will multiply by 1/2 and then when we're done the negative Y will multiply by 1/2 let's go ahead and do that 2x times 1 - 2 x times 2x is 4x squared then you have 2x times negative Y is negative 2xy then you have this negative Y times these two that's again negative 2xy and then you have minus y squared nope plus y squared minus 10 months plus it's important lesson right to not be afraid to make mistakes that comes with the territory fact there's a research that says that making mistakes is the only way that our brains can grow believe this Stanford Research so we can't be afraid to make mistakes because that's the only way our brains will get bigger and bigger by now my brain must be enormous because I make mistakes all the time let's combine like terms in here 4x squared negative 2xy negative 2 X Y is minus 4 X y plus y squared ok it's problems halfway done because we have one more 2x minus y to go now we're welcome to write it to the left or the right of this thing all right from experience I've noticed that writing it at the front is a little smoother explain why ok let's make a little space for ourselves take this off okay bring this up just as a note I do I have had students before that like to write really small and they think they're saving paper or something like that and I remember my dad when I used to do that when I was a kid he'd be like use paper and he would say like your education is worth it that's what you would say so don't be afraid to really stretch out and write it large and in charge your education is worth it as long as you're using the paper to help you learn then that's what it's for right we're not advocating to waste any paper but you really want to spread it out on the page so it minimizes mistakes and it's not as stressful ok so you'll notice I'm trying to write it really big for myself as well or just use white boards okay here we go distributive property 2 times 1 2 3 I'm gonna do it 2x times 4x squared is 8x to the power of 3 cubed 2x times negative 4 X Y is negative 8x squared Y that's these two and then you have 2x times y squared is 2x y squared plus 2x Y squared all right half done now we're gonna keep an eye on negative Y times those 3 all right here they go I'm going to do that in blue actually negative Y times 4x squared is negative 4x squared Y some students write it all out on the line you're welcome to do that all right I'm going to show you a cool stacking technique to help you keep track of all of the like terms so again this would be negative 4x squared Y that's right here minus 4x squared Y it's kind of cool so ready to add down and then you have negative Y times negative 4 X Y that'll be over here plus 4 X Y squared and then we have negative Y times positive y squared that's negative Y cubed it's out here all right and then we're just gonna add down and this problem is complete nice 8 X cubed minus 12x squared y plus 6x y squared minus y cubed all right so basically it was the first two things that we said above the first in the last and this middle action okay so don't forget that when you're squaring or multiplying binomials two terms to write them out and distribute them through all right thank you for watching this is Robert from the a mass org and we'll see you again bye [Music]