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# Simplifying polynomials

CCSS.Math:

## Video transcript

simplify 3x squared minus 8x plus seven plus two x to the third minus x squared plus 8x minus three so when they simplify this we're essentially just going to add up like terms it just shows reminder we can only add or subtract like terms or simplify like terms and just a reminder what I mean by that if I add 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 then I have another x squared well then I have two X Squared's this is two x Squared's if I have an X to the third let's say I have three X to the third plus another four X to the third well that means I have seven X to the thirds seven X to the third 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 simplify these are not like terms just because they both have X's the X's are not - they are not to the same degree so with that in mind let's look at the X's that are 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 to or subtracted to anything else so let's just write that down so we have the two X to the third and then let's look at the x squared terms we have three x squared term we have three x squared over there and then we have a minus we have a what we could view it as a negative x squared over there so if we want to simplify it we can add these two terms we can add we can add let me just write it down so we can add 3x squared - negative x squared so I've just I'm just rearranging it really right now but I'm putting the like terms next to each other so it'll be easy to simplify now let's water it worry about just the X to the first terms or just the X term so 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 could view those is times X to the zeroth power and the constant terms are you have a positive seven over here so plus seven and then you have a negative three over here you have a negative three so all I've done is I've really just used the commutative property of addition to just to change the order or addition and subtraction to change the order at which I'm doing this but I've just rearranged the thing so that 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 that same blue color if we have 3x squared and from that we're taking away an x squared but we're only going to have 2x squared left so that's going to be plus 2x squared and then over here if we have negative eight X's and then we add a Texas to it or you could actually swap these around and you could view it as you are subtracting you are subtracting 8x from positive 8x well though it's just going to cancel out so that's just going to be 0 I could write a plus 0 here but that'd just be redundant wouldn't change the value and then finally I have a plus seven minus three 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 2x squared plus 4