first open the parentheses correctly (watching for that "-" operator), then simply add together degree-and-variable-identical terms (i.e 4x^2 and -2x^2 because the x^2 are identical) hope you understood that

Why it's -15d³-9d³f³-5f³ instead of -24d³-4f³? -15d³ and -9d³ is like terms! -5f³ and f³ is also like terms! It could be simplify more!

The middle term is: `- 9d³f³`. You can't split this term into 2 terms. It is `-9d³ time f³`. You are trying to change it into `9d³ + f³` Addition is not the same as multiplication. Hope this helps.

Where does the +7 go to when you add or subtract the parentheses?

Em, If you are asking about the first practice problem, the `-7` and the `+7` cancel each other `-7 + 7 = 0`

Does this get better with practice? When subtracting, if the subtraction sign (or negative sign) is outside of a parenthesis, I distribute the negative sign to each of the terms inside the parenthesis, but sometimes mistake the sign. When rewriting a problem without parenthesis I mistake the degree, e.g. x^4 is correct but I may write x^2, and I am not aware of the mistake until I check my math.

Yes, everything in math will get better with practice! Basically what he is doing is also known as the Distributive law. You can look it up online but basically, it is actually just multiplying every term in the bracket with a number (can be a negative or a positive number). Therefore, for example -(x^4+3x-6) can be written as -1 (x^4+3x-6), both are equivalent. And recall that when we multiply, the rules on whether the result will have a positive or negative sign when there is a negative number involved in the equation is that; 1) when there is an even number of negative number being multiplied, the result will always be a positive number. 2) if there is an odd number of negative number being multiplied, the result will always be a negative number. Mistaking the degree is part of human error or aka careless mistake, for mistakes like this, just check through your working again before submitting your answer

Main content

Algebra (all content)

Course: Algebra (all content) > Unit 10

Lesson 3: Adding & subtracting polynomials: two variables

Adding and subtracting polynomials with two variables review

CCSS.Math:

HSA.APR.A.1

Google Classroom

Adding and subtracting polynomials is all about combining like terms. When the terms have two variables, it gets a little bit tricky to figure out which terms are like terms. In this article, we review some examples and give you a chance for you to practice the skill yourself.

Adding and subtracting polynomials is all about combining like terms. The polynomials in this article have two variables, which makes figuring out which terms are like terms a little more difficult.

Example 1

Simplify.

left parenthesis, minus, 7, d, cubed, minus, 5, d, cubed, f, cubed, minus, 3, f, cubed, right parenthesis, minus, left parenthesis, 8, d, cubed, plus, 4, d, cubed, f, cubed, plus, 2, f, cubed, right parenthesis

Rewrite without parentheses:

start color #11accd, minus, 7, d, cubed, minus, 5, d, cubed, f, cubed, minus, 3, f, cubed, end color #11accd, start color #ca337c, minus, 8, d, cubed, minus, 4, d, cubed, f, cubed, minus, 2, f, cubed, end color #ca337c

Group like terms:

left parenthesis, start color #11accd, minus, 7, d, cubed, end color #11accd, start color #ca337c, minus, 8, d, cubed, end color #ca337c, right parenthesis, plus, left parenthesis, start color #11accd, minus, 5, d, cubed, f, cubed, end color #11accd, start color #ca337c, minus, 4, d, cubed, f, cubed, end color #ca337c, right parenthesis, plus, left parenthesis, start color #11accd, minus, 3, f, cubed, end color #11accd, start color #ca337c, minus, 2, f, cubed, end color #ca337c, right parenthesis

Simplify:

minus, 15, d, cubed, minus, 9, d, cubed, f, cubed, minus, 5, f, cubed

Example 2

Simplify.

left parenthesis, u, squared, plus, 5, u, squared, v, plus, 4, u, v, squared, right parenthesis, minus, left parenthesis, u, squared, plus, 5, u, squared, v, squared, plus, 4, u, v, right parenthesis

Rewrite without parentheses:

start color #11accd, u, squared, plus, 5, u, squared, v, plus, 4, u, v, squared, end color #11accd, start color #ca337c, minus, u, squared, minus, 5, u, squared, v, squared, minus, 4, u, v, end color #ca337c

Group like terms:

left parenthesis, start color #11accd, u, squared, end color #11accd, start color #ca337c, minus, u, squared, end color #ca337c, right parenthesis, start color #11accd, plus, 5, u, squared, v, plus, 4, u, v, squared, end color #11accd, start color #ca337c, minus, 5, u, squared, v, squared, minus, 4, u, v, end color #ca337c

Simplify:

minus, 5, u, squared, v, squared, plus, 5, u, squared, v, plus, 4, u, v, squared, minus, 4, u, v

Want to see another example? Check out this video.

Practice

Problem 1

Current

Simplify.

left parenthesis, minus, 2, x, start superscript, 4, end superscript, plus, 7, x, squared, y, minus, 7, right parenthesis, plus, left parenthesis, minus, 9, x, cubed, plus, 7, x, y, plus, 7, right parenthesis

Want more practice? Check out this exercise.

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El Ouadi, Jordan
Posted 6 years ago. Direct link to El Ouadi, Jordan's post “how you do this”
how you do this
Button navigates to signup pageComment on El Ouadi, Jordan's post “how you do this”
(5 votes)
Answer
- Eric Parker
  Posted 6 years ago. Direct link to Eric Parker's post “first open the parenthese...”
  first open the parentheses correctly (watching for that "-" operator), then simply add together degree-and-variable-identical terms (i.e 4x^2 and -2x^2 because the x^2 are identical)
  hope you understood that
  Button navigates to signup page
  (16 votes)
💎Chυcκ Lørrε💎
Posted 5 years ago. Direct link to 💎Chυcκ Lørrε💎's post “Why it's -15d³-9d³f³-5f³ ...”
Why it's -15d³-9d³f³-5f³ instead of -24d³-4f³? -15d³ and -9d³ is like terms! -5f³ and f³ is also like terms! It could be simplify more!
Button navigates to signup pageButton navigates to signup page
(5 votes)
Answer
- Kim Seidel
  Posted 5 years ago. Direct link to Kim Seidel's post “The middle term is: `- 9d...”
  The middle term is: - 9d³f³. You can't split this term into 2 terms.
  It is -9d³ time f³. You are trying to change it into 9d³ + f³
  Addition is not the same as multiplication.
  Hope this helps.
  Comment on Kim Seidel's post “The middle term is: `- 9d...”
  (5 votes)
GIANNA TERITO
Posted 2 years ago. Direct link to GIANNA TERITO's post “how do i solve this witho...”
how do i solve this without getting confused
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(2 votes)
Answer
- nr0193954
  Posted 2 years ago. Direct link to nr0193954's post “I know it looks very conf...”
  I know it looks very confusing when simplifying these polynomials. However, what I would do is try to solve the equation like I would with any other expression dealing with polynomials. Most importantly, I would carefully analyze the expression mostly for the signs. This is because not doing so can mess up everything and therefore make you more confused.
  Comment on nr0193954's post “I know it looks very conf...”
  (1 vote)
Jacoblevin
Posted 5 years ago. Direct link to Jacoblevin's post “when you put them in orde...”
when you put them in order which would go first say

4g^2h . or 4gh^2
Button navigates to signup pageComment on Jacoblevin's post “when you put them in orde...”
(1 vote)
Answer
Carter Hooks
Posted 6 months ago. Direct link to Carter Hooks's post “what is the degree and le...”
what is the degree and leading coefficient of 2x^2 y - 7x^2 y^3 +6xy^2
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(1 vote)
Answer
Savannah Pettry
Posted 4 years ago. Direct link to Savannah Pettry's post “Where does the +7 go to w...”
Where does the +7 go to when you add or subtract the parentheses?
Button navigates to signup pageButton navigates to signup page
(0 votes)
Answer
- AD Baker
  Posted 4 years ago. Direct link to AD Baker's post “Em, If you are asking a...”
  Em,
  
  If you are asking about the first practice problem, the -7 and the +7 cancel each other
  
  -7 + 7 = 0
  Button navigates to signup page
  (3 votes)
Marty Rogers
Posted 4 years ago. Direct link to Marty Rogers's post “Does this get better with...”
Does this get better with practice? When subtracting, if the subtraction sign (or negative sign) is outside of a parenthesis, I distribute the negative sign to each of the terms inside the parenthesis, but sometimes mistake the sign. When rewriting a problem without parenthesis I mistake the degree, e.g. x^4 is correct but I may write x^2, and I am not aware of the mistake until I check my math.
Button navigates to signup pageButton navigates to signup page
(0 votes)
Answer
- Quinn
  Posted 4 years ago. Direct link to Quinn's post “Yes, everything in math w...”
  Yes, everything in math will get better with practice!
  
  Basically what he is doing is also known as the Distributive law. You can look it up online but basically, it is actually just multiplying every term in the bracket with a number (can be a negative or a positive number).
  
  Therefore, for example -(x^4+3x-6)
  can be written as -1 (x^4+3x-6), both are equivalent.
  
  And recall that when we multiply, the rules on whether the result will have a positive or negative sign when there is a negative number involved in the equation is that;
  1) when there is an even number of negative number being multiplied, the result will always be a positive number.
  2) if there is an odd number of negative number being multiplied, the result will always be a negative number.
  
  Mistaking the degree is part of human error or aka careless mistake, for mistakes like this, just check through your working again before submitting your answer
  Button navigates to signup page
  (2 votes)
Brenna
Posted 6 years ago. Direct link to Brenna's post “would -2x^4-9x^3+xy be th...”
would -2x^4-9x^3+xy be the answer
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(0 votes)
Answer
- Taryn Stover
  Posted 5 years ago. Direct link to Taryn Stover's post “−2x ^4−9x ^3+7x ^2y+7xy w...”
  −2x ^4−9x ^3+7x ^2y+7xy would be the answer you added wrong, try to go back through and work out the problem again to find your mistake, or click on the explain button to help you!
  Button navigates to signup page
  (0 votes)