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# Adding & subtracting multiple polynomials

CCSS.Math:

## Video transcript

we're asked to simplify this huge long expression here X to the third plus three X minus six that's in parentheses plus negative two x squared plus X minus 2 and then minus the quantity 3x minus four so a good place to start will just rewrite this and see if we can eliminate the prep the parentheses in this step so we'll just start at the beginning we have the X to the third right over there so X to the third and then plus three X I'll do that in pink plus three X plus three X and then we have a minus six minus six now we don't have to put the parentheses around there that those don't really change anything plus and we don't have to even write these prevent anything with these parentheses we can eliminate them just because there's a positive sign out here we don't have to distribute anything distributing a positive sign doesn't do anything these numbers so then plus we have a negative two x squared so this term right here is negative two x squared or minus x squared and then we have a plus X we have a plus X plus X then we have a minus two and we have a minus two then we have a negative sign times this hold expression so we're going to distribute the negative sign so it's a positive 3x but it's being multiplied by negative one so it's really a negative 3x so minus 3x minus 3x and then you have a negative you can imagine this is a negative one implicitly out here negative one times negative four that's a positive 4 so plus four plus four now we could combine terms of similar degree of the same degree now first we have an X to the third term and I think it's the only third degree term here because we have X being raised to the third power let me just rewrite here we have X to the third and let's look at our x squared terms looks like we only have one we only have this term right here so we have minus 2x squared and then what about our X terms we have a 3x plus an X minus a 3x again so that 3x minus the 3x will cancel out and you're just left with an X so plus X and then finally our constant terms negative six minus two plus four negative six - - gets us to negative eight plus four is negative four negative four and we are done we have simplified the expression now we just have a four term polynomial