[Music] in this video we will identify whether or not an expression is a perfect cube and we will factor the sum and difference of two cubes completely so first let us tell whether the following number is a perfect cube or not so a perfect cube or hindi okay let's start so 8 is it a perfect cube or not yes this is a perfect cube because this is 2 times 2 4 times 2 that is 8. next 25 this is not a perfect cube because this is just a perfect square next 64. this is a perfect cube because of 4 times 4 16 16 times 4 that is 64. and then 40 this is not a perfect cube 27 it's a perfect cube because of 3 raised to 3 so 3 times 3 9 times 3 that is 27 60 is not 125 is a perfect cube because of 5 raised to 3. 5 times 5 25 times 5 that is 125 next 72 is not 216 is a perfect cube because of 6 raised to 3 and then number 10 343 this is also a perfect cube because of seven raised to three next let us try to evaluate each exponential notation so meron d perfect cube so ano ang sagot if we're going to evaluate the following exponential notation so let's have the first one 2 raised to 3 or 2 cube so y and i'm gigging 2 times two that is four times two that is eight so two cubed is equal to eight three cubed so that is three times three nine times three that is twenty seven so three cube is equal to twenty seven four cubed that is four times four sixteen times four that is sixty four so four cubed is equal to sixty four five cubed we have five times five twenty-five times five that is one hundred twenty-five so five raised to three or cubed that is equal to one hundred twenty-five six cubed we have six times six 36 times 6 is 216 and 7 cubed we have 7 times 7 49 times 7 that is 343 so 7 cube is equal to 343 okay so to in this video we will focus on how to factor some and difference of two cubes so first let us focus first on sum of two cubes okay so i'm given i x cube plus y cube sub page x plus y where which is your first term plus last term and then x squared or e e square nothing first term nothing minus the product of first term and last term plus the square of your last term so again x refers to your first term y refers to your last term okay so therefore our factored form kapag and given i x cubed plus y cubed that part and factoring formula i x plus y times x squared minus x y plus y squared let's have an example okay i have here a cube plus 64. so onangagawindapatmaggingx cube plus y cube munasha so we will rewrite this as sum of two cubes so we will have eight raised to three and then four raised to three bucket four cubed so bucket fork is four times four sixteen times four sixty-four so ex terminates okay now we will now supply the missing terms x that is a plus y and then y that is four and then x squared and young x so making a squared minus what is your x a your y is four so it times nothing and mama yeah and then your last term that is y so that is four squared so we will now have the factored form of a plus 4 times a squared minus a times nothing say a times 4 that will become 4a plus 4 squared evaluate not n so four times four that is sixteen next i have here eight b cubed plus twenty seven c s uh c cubed okay first rewrite a sum of two cubes cube y cube pattern okay so itself we will have a product of eight that is two the best so two times two four times two that is eight and then young b so that is b cube next so again atom number i three cassette three times three nine times three twenty seven and then c in a long has okay so again your 2b now will become your x or young first term young trisimo will become your y or jung last term okay so we will now supply the missing terms so following this form or factored form so supply like nothing young x nathan i2b plus y what is your y three c and then x squared so sinusoidal factored form so x squared not n and x naught and i to b and then minus x is to be y is three c eta times nathaniel mamaya and then y your last term is three c so we now have the factored form of two b plus three c times so two times two is four and then b squared minus if the times nothing it was two b times three c so 2 times 3 is 6 and then copy the variables which is bnc and then plus so 3 squared simplifying that in c3 squared that is 3 times 3 kayasha nagging nine and then c squared so we now have two b plus three c times four b squared minus six b c plus nine c squared so eton factored form cube minus y cube factoring formula x minus y x squared plus x y plus y squared x plus x minus minus x y naught plus x y naught okay so again this is our first term young x y y and adding last term and then again just copy the first and last term for your first prada binomial and then square nothing on first term multiply not ten young first and last term and then square oled nothing young last term okay you just have to follow this format or form okay so we now have the factored form x minus y times x squared plus x y plus y squared so this is our factored form it is let's have an example so factoring difference of two cubes so again difference kappa given at an i x cubed minus y cube minus nausea so first 27 c cubed minus d cube so first is you're going to write as difference of two cubes so we will have three c three cassette three times three nine times three it's twenty seven and then sina and then sadie so since the cube long shading we already have cube don salabas so this will serve us our three uh first term and then this is our last term so let us now supply the missing terms using this factoid form okay so supply not n your x is 3c your y or jung last term nothing is d again x squared you'll let so x is 3c and then x 3c times y which is your d and then y is d so let us simplify so we now have 3c minus d times 3c squared so young three not n three c squared three squared is equal to nine because three times three and then c squared plus three c times d so that will become three c d plus d squared next so we have 8 e cubed f raised to 6 minus 125 g cube so first rewrite as difference of two cubes so we now have two because two times two is four times two that is eight and then e cubed and then f squared squared nothing d times three kaya six okay so next 125 that is five because of five times five is 25 times 5 that is 125 and then g in a long because it's only g cubed so again this will be our first term and this will be our last term so let us now supply the missing terms following this factored form so supply not n our x is 2 e f squared our y is 5 g and then x again we have 2 e f squared and then x times y so first we have 2 e f squared and then times y we have 5g and then 5g for our y squared so let us now simplify so we will now have 2ef squared minus 5g times so simplifying that in c2 squared that will become 4 and then e squared f raised to four taiyong ion because f raised to two plus two times five young adding middle term soma gigging ten and then e f raised to two g and then plus 5 squared is 5 times 5 that's why it became 25 and then g squared so this is now our factoid form next i have 64 minus p raised to 6. so rewrite as difference of 2 cubes we have 4 cubed because 4 times 4 16 16 times 4 that is 64. and then since p raised to 6 ito so anu eta times nothing's at 3 but i'm getting 6 so p raised to 2. so again 4 is our first term y is our last term supply the missing terms using this factored form so we now have our x which is four y is p squared x again is four and then x y we have four n p squared and then y is p squared so we now have the factored form 2 plus p times 2 minus p because 4 minus p squared is the sum and difference of two squared okay so four minus p squared is the sum and difference of two squares so okay and then four squared is four times four that is sixteen plus four p squared eta times not in sha and then p raised to 2 times raised to 2 so that will become p raised to 4. so this is now our factored form 2 plus p times 2 minus p times 16 plus 4 p squared plus four p raised to no p raised to four thank you for watching this video i hope you learned something don't forget to like subscribe and hit the bell button to our walmart channel just keep on watching