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### 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

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# Subtracting polynomials: two variables (intro)

Sal simplifies (4x²y - 3xy + 25) - (9y²x + 7xy - 20). Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

- IS 4x^2y - 10xy - 9y^2x + 45 also acceptable? ...... I just swopped two of the terms around.(6 votes)
- Ideally, you'd write it in order of decreasing powers with the variable first in alphabetical order. Sadly, it gets more complicated with multiple variables and when you have different powers.

Personally, I'd write it like you did: The x's are in order of decreasing power, and the y's highest power is after the one with y^1. Just personal preference really. I would never say it's wrong if you write it in a different order: it's just how you interpret your answer.

Hope I helped!(14 votes)

- Why does he put his answers in that order?(8 votes)
- It is in polynomial standard form which is from highest to lowest exponent value.(1 vote)

- isn't negative 3 minus seven suppose to be negative 7 because the 7 is followed by a minus sign?(4 votes)
- in my answer i got -5x^2y-10xy+45

i thought that because 4x^2y-9x^2y would equal -5x^2y

but instead he counted them as two different like terms,

why is that?(3 votes)- saeed, I think you misread. That second term is (-9)y^2x - the y is squared not the x. The terms are not like terms.(6 votes)

- At0:26, why did Sal wrote a number 1 in between of the quantities? What is the purpose of that?

(4x²y - 3xy + 25) -`1`

(9y²x + 7xy - 20)(5 votes)- Just to show that it is a negative one for all number in the parentheses instead of just the first number.(3 votes)

- what if the question is like 9xy - 12yx. what would u do here. would these be considered as LIKE TERMS(4 votes)
- Yes they're like terms and should be simplified. You won't get marked wrong(4 votes)

- How do you write this in standard form for this? Which variable comes first?(2 votes)
- The most common way is seen polynomials arranged is to have the highest power of the lowest letter of the variables go first and then arrange the remaining items in a "descending" order where the constant is the last item in the arrangement. You don't have to arrange it on any particular order. We can arrange them however we want due to the commutativity of addition. What really matters is that you can tell the difference between the terms and understand that objects like (x^2)(y) and (x)(y^2) are not necessarily the same thing. Hope this helps. Good luck!(5 votes)

- if you add x and x together does that make x^2(1 vote)
- When you add two like terms, you always combine the co-factors. x + x would produce 2x rather than x^2. However, x*x will produce x^2(1 vote)

- I am confused. Like what would be the answer if you did x to the fourth power plus x to the 3rd power(3 votes)
- You would be left with x^4 + x^3. You are unable to add different powers of the same variable. The order of operations states that exponents must be evaluated before addition, but since the exponent cannot be evaluated without knowing the value of x, the addition cannot be done either.(1 vote)

- please explain how to work out the following 1/3 (3a + 2) + 1/4 (4a-2)(2 votes)
- 1st change 4a-2 to 4a+ (-2)

1/3 (3a + 2) + 1/4 (4a + (-2))

Then distribute 1/3.

1/3*3a + 1/3*2 + 1/4 (4a + (-2))

Simplify.

a + 2/3 + 1/4 (4a + (-2))

Then distribute 1/4.

a + 2/3 + 1/4*4a + 1/4*(-2)

Simplify

a + 2/3 + a + (-2/4)

Combine like terms: a + a & 2/3 + (-2/4)

Fractions must have common denominators to find the sum, 2/3 =4/6 & -2/4 = -3/6, therefore 4/6 + (-3/6) = 1/6.

2a +1/6(2 votes)

## Video transcript

We've got 4x squared
y minus 3xy plus 25 minus the entire expression 9y
squared x plus 7xy minus 20. So when we're subtracting
this entire expression, that's equivalent to
subtracting each of these terms individually if we didn't
have the parentheses. Or another way of
thinking about it-- we could distribute
this negative sign. Or you could view this
as a negative 1 times this entire expression. And we can distribute it. So let's do that. So let me write this
first expression here. I'm going to write it unchanged. So it is 4x squared
y minus 3xy plus 25. And now let me distribute
the negative 1, or the negative sign
times all of this stuff. So negative 1 times 9y squared
x is negative 9y squared x. Negative 1 times
7xy is negative 7xy. And then negative 1
times 20 is positive 20. And now we just have
to add these terms. And we just want to
group like terms. So let's see, is there another
x squared y term anywhere? No, I don't see one. So I'll just rewrite this. So we have 4x squared y. Now, is there another xy term? Yeah, there is. So we can group negative
3xy and negative 7xy. Negative 3 of something minus
another 7 of that something is going to be negative
10 of that something. So it's negative 10xy. And then we have a 25, which
is just a constant term. Or an x to the 0 term. It's 25x to the 0. You could view it that way. And there's another constant
term right over here. We can always add 25 to 20. That gives us 45. And then we have this
term right over here, which clearly can't be
merged with anything else. So minus 9y squared. Let me do that in
that original color. Minus 9-- I'm having
trouble shifting colors-- minus 9y squared x. And we are done.