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## Algebra (all content)

### Course: Algebra (all content) > Unit 10

Lesson 2: Adding & subtracting polynomials- Adding polynomials
- Add polynomials (intro)
- Subtracting polynomials
- Subtract polynomials (intro)
- Polynomial subtraction
- Adding & subtracting multiple polynomials
- Add & subtract polynomials
- Adding polynomials (old)
- Adding and subtracting polynomials review

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# Adding & subtracting multiple polynomials

Sal simplifies (x³ + 3x - 6) + (-2x² + x - 2) - (3x - 4). Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

- on khan how can i enter an answer with an exponent? im having trouble entering exponents.(6 votes)
- Usually, a little tab pops up underneath the answer text box with different math operations and symbols such as an exponent.(3 votes)

- At1:31, how can we know if that is a -4 or a minus 4. An how is the product a positive 4? Thanks(2 votes)
- At1:24Sal explains that there is a given number in between the subtraction sign and the parenthesis. In fact at1:27he uses a pink font to draw the 1 into the expression. It is understood that there is an 'invisible' 1 when interpreting negative operations. It is with the use of this understood 1 that we evaluate the expression for simplification. When distributed, -1*-4 equals positive 4.(9 votes)

- G=3t-5t+6

P=-8t^(2)+7t-9

G+P=(3 votes)- Add your 2 polynomials: 3t-5t+6 + (-8t^2)+7t-9

Combine like terms.

Hope this helps.(4 votes)

- When do I know when to subtract and add polynomials.(2 votes)
- When do you know how to add & subtract numbers?

The same symbols are used. You add polynomials when there are plus signs. You subtract them when there is a minus sign. Remember to only add/subtract like terms within the polynomials.(6 votes)

- At2:01Sal cancels out the 3x and -3x and leaves it with just x

But doesn't the whole term cancel out so the final answer would be x^3 - 2x^2 - 4?(2 votes)- There are three terms containing "x"

3x + x - 3x

Yes, 3x and -3x cancel out to 0, but that still leaves the "x" term

Hope this helps.(3 votes)

- What's the difference between adding/subrtracting/multiplying polynomials vertically and horizontally?(3 votes)
- wait so if i have a problem like (2x + 3y - 4) + (x - 3y + 7) and i added all the terms up, which operations do i put into the simplified equation? like for the first term, you add them and it's 3x, but then the two first operations are opposite, for the first one it's + and the second one it's -. so which one do i use in the final answer? please help this assignment is due today.(2 votes)
- Ok, so I know I'm way too late but maybe others have this question too. So when you add the 3y with the -3y they cancel out. Think of it this way: 3 - 3 = 0. So, 3 - 3y = 0. As for adding the -4 and the +7 you do the same thing. Start with the postitive and then subtract the negative. So, 7 - 4 = 3. So... the final answer to this problem is
**3x + 3**(1 vote)

- wait correct me if I'm wrong but in equation x to the third cannot be simplified neither can x squared(2 votes)
- x^3 cannot be simplified. Neither can -2x^2. In this equation, there is no x^2.(0 votes)

- simplify -3a (a+b -5) +4 (-2a + 2b) +b (a+ 3b -7)(1 vote)
- It is just a lot of distributing then combining like terms:

-3a^2 - 3ab + 15a -8a + 8b +ab + 3b^2 - 7b

-3a^2 - 3ab + ab + 3b^2 + 15a - 8a + 8b - 7b

- 3a^2 - 2ab + 3b^2 + 7a + b(2 votes)

- So, how come you didn't change the sign for -2x squared and you changed the sign for 3x? Is there a rule for that?(1 vote)
- The sign on -2x didn't change because it is being added: +(-2x) is still -2x.

The sign changed on 3x because it is being subtracted: -(+3x) = -1(+3x) = -3x

Hope this helps.(2 votes)

## 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.