on khan how can i enter an answer with an exponent? im having trouble entering exponents.

Usually, a little tab pops up underneath the answer text box with different math operations and symbols such as an exponent.

G=3t-5t+6 P=-8t^(2)+7t-9 G+P=

Add your 2 polynomials: 3t-5t+6 + (-8t^2)+7t-9 Combine like terms. Hope this helps.

At 1:31, how can we know if that is a -4 or a minus 4. An how is the product a positive 4? Thanks

At 1:24 Sal explains that there is a given number in between the subtraction sign and the parenthesis. In fact at 1:27 he 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.

When do I know when to subtract and add polynomials.

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.

At 2:01 Sal 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?

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.

simplify -3a (a+b -5) +4 (-2a + 2b) +b (a+ 3b -7)

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

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?

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.

Main content

Algebra (all content)

Course: Algebra (all content) > Unit 10

Lesson 2: Adding & subtracting polynomials

Adding & subtracting multiple polynomials

Name: Adding & subtracting multiple polynomials
Uploaded: 2011-02-20T16:29:22Z
Description: Sal simplifies (x³ + 3x - 6) + (-2x² + x - 2) - (3x - 4).

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

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Adriana V.
Posted 10 years ago. Direct link to Adriana V.'s post “on khan how can i enter a...”
on khan how can i enter an answer with an exponent? im having trouble entering exponents.
Button navigates to signup pageComment on Adriana V.'s post “on khan how can i enter a...”
(6 votes)
Answer
- Cassidy
  Posted 5 years ago. Direct link to Cassidy's post “Usually, a little tab pop...”
  Usually, a little tab pops up underneath the answer text box with different math operations and symbols such as an exponent.
  Button navigates to signup page
  (3 votes)
Petula
Posted 11 years ago. Direct link to Petula's post “At 1:31, how can we know ...”
At
1:31
, how can we know if that is a -4 or a minus 4. An how is the product a positive 4? Thanks
Button navigates to signup pageComment on Petula's post “At 1:31, how can we know ...”
(2 votes)
Answer
- Nancy Janette Chambless
  Posted 10 years ago. Direct link to Nancy Janette Chambless's post “At 1:24 Sal explains that...”
  At
  1:24
  Sal explains that there is a given number in between the subtraction sign and the parenthesis. In fact at
  1:27
  he 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.
  Comment on Nancy Janette Chambless's post “At 1:24 Sal explains that...”
  (9 votes)
Victor, Hernandez
Posted 5 years ago. Direct link to Victor, Hernandez's post “G=3t-5t+6 P=-8t^(2)+7t-9 ...”
G=3t-5t+6
P=-8t^(2)+7t-9
G+P=
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(3 votes)
Answer
- Kim Seidel
  Posted 5 years ago. Direct link to Kim Seidel's post “Add your 2 polynomials: 3...”
  Add your 2 polynomials: 3t-5t+6 + (-8t^2)+7t-9
  Combine like terms.
  Hope this helps.
  Button navigates to signup page
  (4 votes)
mluna51
Posted 6 years ago. Direct link to mluna51's post “When do I know when to s...”
When do I know when to subtract and add polynomials.
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(2 votes)
Answer
- Kim Seidel
  Posted 6 years ago. Direct link to Kim Seidel's post “When do you know how to a...”
  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.
  Comment on Kim Seidel's post “When do you know how to a...”
  (6 votes)
JinLover
Posted 6 years ago. Direct link to JinLover's post “At 2:01 Sal cancels out t...”
At
2:01
Sal 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?
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(2 votes)
Answer
- Kim Seidel
  Posted 6 years ago. Direct link to Kim Seidel's post “There are three terms con...”
  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.
  Button navigates to signup page
  (3 votes)
isaiahgoden
Posted 5 years ago. Direct link to isaiahgoden's post “What's the difference bet...”
What's the difference between adding/subrtracting/multiplying polynomials vertically and horizontally?
Button navigates to signup pageComment on isaiahgoden's post “What's the difference bet...”
(3 votes)
Answer
moon
Posted 4 years ago. Direct link to moon's post “wait so if i have a probl...”
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.
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(2 votes)
Answer
- StudyBuddy
  Posted a year ago. Direct link to StudyBuddy's post “Ok, so I know I'm way too...”
  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
  Button navigates to signup page
  (1 vote)
Dillan Gannetta
Posted 7 years ago. Direct link to Dillan Gannetta's post “wait correct me if I'm wr...”
wait correct me if I'm wrong but in equation x to the third cannot be simplified neither can x squared
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(2 votes)
Answer
- Cassidy
  Posted 5 years ago. Direct link to Cassidy's post “x^3 cannot be simplified....”
  x^3 cannot be simplified. Neither can -2x^2. In this equation, there is no x^2.
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  (0 votes)
Maribel Sastre
Posted 5 years ago. Direct link to Maribel Sastre's post “simplify -3a (a+b -5) +4 ...”
simplify -3a (a+b -5) +4 (-2a + 2b) +b (a+ 3b -7)
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(1 vote)
Answer
- David Severin
  Posted 5 years ago. Direct link to David Severin's post “It is just a lot of distr...”
  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
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  (2 votes)
PinkMalibu
Posted 5 years ago. Direct link to PinkMalibu's post “So, how come you didn't c...”
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?
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(1 vote)
Answer
- Kim Seidel
  Posted 5 years ago. Direct link to Kim Seidel's post “The sign on -2x didn't ch...”
  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.
  Button navigates to signup page
  (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.