Subtracting polynomials: two variables

or ask to subtract negative 6x to the 4th minus 3x squared y squared plus y to the 4th from 2x to the fourth minus 8x squared y squared minus y to the 4th and I encourage you to pause this video and give it a try all right let's work through it together so we're going to subtract this green polynomial from this magenta one so we can rewrite this as or to actually perform it we could write to X to the fourth minus 8x squared y squared minus y to the fourth minus I'm going to write this in parentheses give us some space minus negative six x to the fourth minus three x squared y squared plus five Y to the fourth so notice I'm subtracting this green polynomial and two variables from this magenta polynomial in two variables which is exactly what it says to do up here so what's this going to be well I can just rewrite the magenta part we're going to have 2x to the fourth minus 8x squared y squared minus y to the fourth and then I can distribute this negative sign so if we say the negative of negative 6x to the fourth it's going to be positive 6x to the fourth so it's going to be positive 6x to the fourth and then the negative of negative 3x squared Y squared is going to be positive 3x squared Y squared so plus 3x squared Y squared and then last but not least we have a negative or we're subtracting positive 5y to the fourth so that's going to be subtracting five Y to the fourth or negative five Y to the fourth and now we can try to simplify so let's first look at this this term right over here this is a we have 2x to the fourth and what we could look for is another X to the fourth term and we see it right over here so we have 2 X to the fourths and we can add that to 6 X to the fourth so what's that going to be well if I have to of something and then I add another six of that something that's going to be 8 X to the 4th 2 plus 6 2 X to the 4th plus 6 X to the 4 it's it's going to be 8 X to the 4th power and now we have this x squared Y squared term we have we could say we could say we're subtracting 8 of them and over here we're adding 3 of these x squared Y squared terms so we could add these coefficients if we're taking away 8 but we're adding 3 we could view this as negative 8 x squared Y Squared's plus 3 x squared Y Squared's well it's negative 8 plus 3 well that's going to be negative 5 negative 5 X Squared's Y Squared's so that's that term right that a little bit neater that's this term right over here don't forget to include the sign here this is you're subtracting 8 x squared Y squared so you could view that as negative 8x squared Y squared plus 3 x squared Y squared and then last but not least you have your subtracting 1 Y to the fourth and then you're subtracting 5 more Y to the fourths so what's that going to be so net you could use this negative 1 Y to the fourth minus 5y to the fourth well that's going to be negative 1 minus 5 is negative 6 negative 6 Y to the fourths and we're done we have subtracted this from that