Polynomial subtraction & set closure

we're asked to subtract negative 2x squared plus 4x minus 1 from 6x squared plus 3x minus 9 and like always encourage you to pause the video and see if you can give it a go all right now let's work through this together so I could rewrite this as 6x squared plus 3x minus 9 minus minus this expression right over here so I'll put that in parentheses minus negative 2x squared negative 2x squared plus 4x minus 1 now what can we do from here well we can distribute this negative sign we can distribute this negative sign and then if we did that we would get the 6x squared plus 3x minus 9 won't change so we still have that 6x squared plus 3x minus 9 but if I distribute the negative sign the negative of negative 2x squared is positive 2x squared so that's going to be positive to get a little more space positive 2x squared and then subtract and then the negative of positive 4x is I'm going to subtract 4x now and then the negative of negative 1 or the opposite of negative 1 is going to be positive 1 so I've just distributed the negative sign and now I can add terms that have the same degree on our X are the same degree terms I guess you could say so I have an x squared term here it's 6x squared here I have a 2x squared term so I can add those two together 6x squared plus 2x squared if I have 6 X Squared's and then I have another 2 X Squared's how many X squares am I now going to have I'm now going to have 8 X Squared's 8 X Squared's or 6x squared plus 2x squared we add the coefficients the 6 and the 2 to get 8 8 x squared then we can add the we can add the X terms you could view these as the first degree terms 3x we have 3x and then we have minus 4 so 3x minus 4x if I have three of something and I take away four of them I'm now going to have negative one of that thing so or you could say that the coefficients 3 minus 4 would be negative 1 so I now have negative 1x I could write it as negative 1x but I might as well just write it as negative x that's the same thing as negative 1x and then finally I can deal with our constant terms I have I'm subtracting a 9 and then I'm adding a 1 so you could say well what's negative 9 plus 1 well that's going to be negative 8 that's going to be negative 8 and we are all done