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Current time:0:00Total duration:2:32

Video transcript

let's see if we can factor 36 a to the eighth plus two B to the sixth power and I encourage you to pause the video and try it out on your own so let's see if we can express this or re Express this as the difference of squares using imaginary numbers so we can rewrite 36 as six squared and a to the eighth is the same thing as a to the fourth squared and so let me actually just write it this way we could rewrite it as 6a to the fourth squared that's this first term right over here and then the second term we can write we can write it as actually let me just write it this way first plus I'm just writing as a square plus square root of two B to the third power squared now we wanted to write it as a difference of squares so instead of it writing it this way let's get rid of this plus and let's so let me clear that out and I could write it as subtracting subtracting a negative one times that and negative one we know is the same thing as I squared so we can rewrite this whole thing as 6a to the fourth squared and then we have this minus right over here - and so this is I squared negative 1 is I squared so we can rewrite this in this pink color as I times the square root of 2 times B to the third all of that squared notice I squared is negative 1 square root of 2 squared is 2 B to the third squared is B to the sixth power if I raise something to an exponent then raise it to another exponent I would multiply the two exponents and so now I've expressed it as a difference of squares there's a difference of squares so we're ready to factor this is going to be equal to 6 a to the fourth minus minus minus I times the square root of 2 times B to the third times and let me get myself some space here times six a to the fourth six a to the fourth plus plus all of this business I times the square root of two times B to the third power and we are done