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

Lesson 3: Adding & subtracting polynomials: two variables

# Adding and subtracting polynomials with two variables review

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.
$\left(-7{d}^{3}-5{d}^{3}{f}^{3}-3{f}^{3}\right)-\left(8{d}^{3}+4{d}^{3}{f}^{3}+2{f}^{3}\right)$
Rewrite without parentheses:
$-7{d}^{3}-5{d}^{3}{f}^{3}-3{f}^{3}-8{d}^{3}-4{d}^{3}{f}^{3}-2{f}^{3}$
Group like terms:
$\left(-7{d}^{3}-8{d}^{3}\right)+\left(-5{d}^{3}{f}^{3}-4{d}^{3}{f}^{3}\right)+\left(-3{f}^{3}-2{f}^{3}\right)$
Simplify:
$-15{d}^{3}-9{d}^{3}{f}^{3}-5{f}^{3}$

## Example 2

Simplify.
$\left({u}^{2}+5{u}^{2}v+4u{v}^{2}\right)-\left({u}^{2}+5{u}^{2}{v}^{2}+4uv\right)$
Rewrite without parentheses:
${u}^{2}+5{u}^{2}v+4u{v}^{2}-{u}^{2}-5{u}^{2}{v}^{2}-4uv$
Group like terms:
$\left({u}^{2}-{u}^{2}\right)+5{u}^{2}v+4u{v}^{2}-5{u}^{2}{v}^{2}-4uv$
Simplify:
$-5{u}^{2}{v}^{2}+5{u}^{2}v+4u{v}^{2}-4uv$
Want to see another example? Check out this video.

## Practice

Problem 1
Simplify.
$\left(-2{x}^{4}+7{x}^{2}y-7\right)+\left(-9{x}^{3}+7xy+7\right)$

Want more practice? Check out this exercise.

## Want to join the conversation?

• how you do this
• 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.
• how do i solve this without getting confused
(1 vote)
• 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.
(1 vote)
• when you put them in order which would go first say

4g^2h . or 4gh^2
• what is the degree and leading coefficient of 2x^2 y - 7x^2 y^3 +6xy^2
• 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
• would -2x^4-9x^3+xy be the answer
• −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!
• 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.