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# Adding & subtracting multiple polynomials

Video transcript

We're asked to simplify this
huge, long expression here. x to the third plus 3x minus 6--
that's in parentheses-- plus negative 2x squared
plus x minus 2. And then minus the quantity
3x minus 4. So a good place to start, we'll
just rewrite this and see if we can eliminate the
parentheses in this step. So let's just start
at the beginning. We have the x to the third
right over there. So x to the third and then
plus 3x-- I'll do that in pink-- plus 3x. And then we have a minus 6. And we don't have to put the
parentheses around there, those don't really
change anything. And we don't have to even write
these-- do 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 to these numbers. So then plus, we have a
negative 2x squared. So this term right here
is negative 2x squared, or minus x squared. And then we have a plus x. We have a plus x. Then we have a minus 2. Then we have a negative sign
times this whole expression. So we're going to have to
distribute the negative sign. So it's a positive 3x, but
it's being multiplied by negative 1. So it's really a negative 3x. So minus 3x, then you have a
negative-- you can imagine this is a negative 1 implicitly
out here-- negative 1 times negative 4. That's a positive 4. So plus 4. 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. So let me just rewrite
it here. We have x to the third. And now 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 would
cancel out, and you're just left with an x. So plus x. And then finally our constant
terms. Negative 6 minus 2 plus 4. Negative 6 minus 2 gets
us to negative 8. Plus 4 is negative 4. And we are done. We have simplified
the expression. Now we just have a four
term polynomial.