Main content
Course: Algebra (all content) > Unit 10
Lesson 3: Adding & subtracting polynomials: two variables- Adding polynomials: two variables (intro)
- Subtracting polynomials: two variables (intro)
- Add & subtract polynomials: two variables (intro)
- Subtracting polynomials: two variables
- Add & subtract polynomials: two variables
- Finding an error in polynomial subtraction
- Add & subtract polynomials: find the error
- Polynomials review
- Adding and subtracting polynomials with two variables review
© 2024 Khan AcademyTerms of usePrivacy PolicyCookie Notice
Subtracting polynomials: two variables
Sal subtracts -6x⁴-3x²y²+5y⁴ from 2x⁴-8x²y²-y⁴.
Want to join the conversation?
at3:20aren't you supposed to write the exponents in descending order? So it would be 8X to the fourth power minus 6Y to the fourth power minus 5X squared Y squared.(3 votes)
When terms have multiple variables, the degree is the sum of the exponents; therefore 5x^2y^2 also has a degree of 4. Another example would be that 3xy^2 has a degree of 3, since the "x" is actually x^1.
I don't know for sure if there's a rule for ordering terms with the same degree (and different variables), though, so hopefully someone else can clear that up.(6 votes)
When Sal says "plus y to the fourth", he really meant to say "plus 5y to the fourth. Just wanted to inform anyone who is confused about that!(5 votes)
What would be a good website for practicing integer rules alongside polynomials?(3 votes)
ixl, or worksheets from grade 9/grade 8 excerpts would work great!(1 vote)
Why doesn't Sal put the final answer in standard form?(2 votes)
All the terms in the polynomial are degree 4, so the polynomial is in standard form since there is no higher / lower degree.(3 votes)
How come he didn't write it in standard form?(1 vote)![winston default style avatar for user P®[]G®@/\/\/\/\|/\/G /\/\@$†∑®](https://cdn.kastatic.org/images/avatars/svg/cs-winston.svg)
if a term Ax^(non-negative integer)? Why is -8x^2y^2? Won't that be Ax^(non-negative integer)x^(non-negative integer). Or can is just keep going on like that and still be a term.
If so, it seems that polynomials are nearly any number not raised to a negative power, so what's the point of polynomials. It seems like a pretty wide classification (like a rational numbers), but then why are we learning so much about them? I get the whole 'under subtraction' concept but is that the only reason. Or is there allot more you can do with them later. (This question will probably be answered when I finish learning about it, but I would like the help all the same)
Is there something I don't understand, or will they just talk about it later?(2 votes)- You say it’s in standard form but x^2 and y^2 are different variables. You can’t combine them. Please correct me if I’m wrong(1 vote)
You are right that x^2 and y^2 are different variables. However, when putting them directly next to each other, we don't know what x and y are equal to. That is why we leave them directly next to each other. I hope this helps.(1 vote)
Why is there not an Adding polynomials: two variables challenge? And is there a reason to not include problems with more variables and exponents? Now don't get me wrong, I personally want to stay away from polynomials with so many terms that feature like 4-5 variables and 3-4 exponents. But I'm finding them more and more in what I'm learning in algebra 1 and want to be equipped to deal with them without my brain shutting off. Otherwise on the final, I'm screwed and have to repeat Algebra 1 again. AND I'M SICK OF ALGEBRA 1! :'( I do hope I'm not coming off as ugly or any way insensitive, but omgosh! Algebra has been killing me. And I want to be able to study well enough to get through it finally because I've had to repeat it like 4-5 times. I want out of it so bad, if it wasn't required to get through college I'd already have jumped ship.(1 vote)
When is subtracting you always have to switch the places of the polynomials ?(1 vote)- Does it matter what order the terms are in once simplified? I thought it said to put them in standard form yet when I do I get them wrong.(1 vote)
3:20Video transcript
- [Voiceover] We're asked
to subtract negative six X to the fourth minus
three X squared Y squared plus Y to the fourth from
two X to the fourth minus eight X squared Y squared
mins Y to the fourth. And I encourage you to pause
this video and give it a try. Alright, let's work through it together. So We're gonna subtract
this green polynomial from this magenta one. So we can rewrite this as, we're to actually
perform it we could write two X to the fourth minus eight X squared Y squared minus Y to the fourth minus, and I'm gonna
write this in parenthesis, give us some space, minus negative six X to the fourth minus three X squared Y squared plus five Y to the fourth. So notice, I'm subtracting
this green polynomial in two variables from
this magenta polynomial in two variables. Which is exactly what
it says to do up here. So what's this going to be? Well I can just rewrite the magenta part. We're gonna have two X to the fourth minus eight X squared Y squared minus Y to the fourth. And then I can distribute
this negative sign. So if we say the negative of
negative six X to the fourth, that's gonna be positive
six X to the fourth. So that's gonna go positive
six X to the fourth. And then the negative of negative
three X squared Y squared is going to be positive
three X squared Y squared. So plus three X squared Y squared. And then last but not least, we have a negative, or we're subtracting positive five Y to the fourth. So that's going to be
subtracting five Y to the fourth, or negative five Y to the fourth. And now we can try to simplify. So let's first look at
this term right over here. We have two X to the fourths. And what we could look for is
another X to the fourth term. And we see it right over here. So we have two X to the fourths and we can add that to
six X to the fourths. So what's that going to be? Well if I have two of something,
and then I add another six of that something, that's going to be eight X to the fourths, two plus six. Two X to the fourth
plus six X to the fourth is going to be eight
X to the fourth power. And now we have this X
squared Y squared term. We could say we're
subtracting eight of them. And over here we're adding three of these X squared Y squared terms. So we could add these coefficients. If we're taking away eight,
but we're adding three we could view this as negative
eight X squared Y squareds plus three X squared Y squareds. Well what's negative eight plus three? Well that's going to be negative five. Negative five X squareds Y squareds. So that's that term. Let me write that a little bit neater. That's this term right over here, don't forget
to include this sign here. This is you're subtracting
eight X squared Y squareds, you could do that as negative
eight X squared Y squared plus three X squared Y squared. And then last but not least, you're subtracting one Y to the fourth, and then you're subtracting
five more Y to the fourths. So what's that going to be? You could view this as
negative one Y to the fourth minus five Y to the fourths. Well that's going to be
negative one minus five is negative six. Negative six Y to the fourths. And we're done, we have subtracted this from that.