Adding & subtracting multiple polynomials
About this video
Sal simplifies (x^3 + 3x - 6) + (-2x^2 + x - 2) - (3x - 4). He removes the parentheses after a plus sign directly, distributes the negative sign over (3x - 4), and combines like terms to get x^3 - 2x^2 + x - 4.
You'll be able to
- remove parentheses when a polynomial is added.
- distribute a negative sign when a polynomial is subtracted.
- combine like terms to simplify several polynomials.
Key words
- distribute
- Multiply a number or sign outside parentheses by every term inside them.
- degree
- The power on the variable in a term, such as 3 for x^3.
- constant term
- A term with no variable, like -6 or 4.
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.
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