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Simplifying polynomials

Simplifying the polynomial 3x²-8x+7+2x³-x²+8x-3 by combining like terms. Created by Sal Khan.

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Video transcript

simply 3x squared minus 8x plus 7 plus 2x to the third minus x squared plus eight x minus 3 so when we simplify this we're essentially going to add up like terms and just as a reminder we can only add or subtract like terms or simplify like terms and just a reminder and what I mean by that if I had an x squared to an x squared these are like terms they're both x terms raised to the same power the same degree so if I have one x squared and another x squared well then I have 2x squared - this is 2x squared If I have an x to the third - let's say I have 3x to thirds plus another 4x to the thirds Well that means I have 7x to the thirds - 7x to the thirds I can't take an x squared and add it to an x to the third I cannot simplify this in any way, so this you cannot simplify cannot simply - these are not like terms just because they both have Xs The Xs are not to - they are not to the same degree With that in mind let's look at the Xs to the same degree Let's start with the highest degree So the highest degree or the highest exponent on an x here - is actually this x to the third here but it looks like the only one it's the only place where we're raising x to the third power so that can't be merged or added or subtracted to anything else so let's just write that down. so we have 2x to the third and let's look at the x squared terms. We have 3x squared over there and we have a minus or we can view as a negative x squared over there so if we want to simplify we can add these two terms - we can add- so let me just write it down we can add 3x squared to negative x squared so I'm just rearranging it really right now I'm putting the like terms next to each other so it'll be easy to simplify now let's just worry about the x to the first terms or just the x terms you have a negative 8x term right over here so let me write it over here negative 8x and then you have a positive 8x term right over here, so let me write that down so positive 8x and then finally let's look at the constant terms you can view those as times x to the zeroth power and the constant terms are - you have a positive 7 over here - so plus 7 and then you have a negative 3 over here you have a negative 3 so all I'll I've done is I've really just used the communative property of addition to just change the order - or addition and subtraction - to change the order in which I'm doing this I've just rearranged the things so the like terms are next to each other but now we can simplify so we have 2x to the third - nothing to simplify that with but then if we subtract - if we have - let me do that in the same blue color if we have 3x squared and from that we're taking away an x squared well, we're only gonna have 2x squared left so that's gonna be plus 2x squared and then over here if we have negative 8 Xs and then we add 8 Xs to it or you can actually swap these around you could view it as you are subtracting 8 x from positive 8x we'll those are just going to cancel out so it's just going to be zero - I could just write plus zero here, but that'd just be redundant it wouldn't change the value and then finally I have a plus 7 minus 3 well that is just clearly 7 minus 3 is 4 so I have plus 4 And we're done! We've simplified it! 2x to the third plus 2 x squared plus 4