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Study Guides > Prealgebra

Adding and Subtracting Polynomials

Learning Outcomes

  • Add polynomials
  • Subtract polynomials
  In The Language of Algebra, you simplified expressions by combining like terms. Adding and subtracting monomials is the same as combining like terms. Like terms must have the same variable with the same exponent. Recall that when combining like terms only the coefficients are combined, never the exponents.  

example

Add: [latex]17{x}^{2}+6{x}^{2}[/latex]. Solution
[latex]17{x}^{2}+6{x}^{2}[/latex]
Combine like terms. [latex]23{x}^{2}[/latex]
 

try it

[ohm_question]146075[/ohm_question]
   

example

Subtract: [latex]11n-\left(-8n\right)[/latex].

Answer: Solution

[latex]11n-\left(-8n\right)[/latex]
Combine like terms. [latex]19n[/latex]

 

try it

[ohm_question]146315[/ohm_question] [ohm_question]146077[/ohm_question]
 

example

Simplify: [latex]{a}^{2}+4{b}^{2}-7{a}^{2}[/latex].

Answer: Solution

[latex]{a}^{2}+4{b}^{2}-7{a}^{2}[/latex]
Combine like terms. [latex]-6{a}^{{}^{2}}+4{b}^{2}[/latex]
Remember, [latex]-6{a}^{2}[/latex] and [latex]4{b}^{2}[/latex] are not like terms. The variables are not the same.

 

try it

[ohm_question]146078[/ohm_question]
Watch the following video for more examples of how to multiply polynomials. https://youtu.be/KYZR7g7QcF4

Add and Subtract Polynomials

Adding and subtracting polynomials can be thought of as just adding and subtracting like terms. Look for like terms—those with the same variables with the same exponent. The Commutative Property allows us to rearrange the terms to put like terms together. It may also be helpful to underline, circle, or box like terms.  

Example

Find the sum: [latex]\left(4{x}^{2}-5x+1\right)+\left(3{x}^{2}-8x - 9\right)[/latex].

Answer: Solution

[latex]\left(4{x}^{2}-5x+1\right)+\left(3{x}^{2}-8x - 9\right)[/latex]
Identify like terms. .
Rearrange to get the like terms together. .
Combine like terms. [latex]7x^2-13x-8[/latex]

 

try it

[ohm_question]146084[/ohm_question]
  Parentheses are grouping symbols. When we add polynomials as we did in the last example, we can rewrite the expression without parentheses and then combine like terms. But when we subtract polynomials, we must be very careful with the signs.  

example

Find the difference: [latex]\left(7{u}^{2}-5u+3\right)-\left(4{u}^{2}-2\right)[/latex].

Answer: Solution

[latex]\left(7{u}^{2}-5u+3\right)-\left(4{u}^{2}-2\right)[/latex]
Distribute and identify like terms. .
Rearrange the terms. .
Combine like terms. [latex]3{u}^{2}-5u+5[/latex]

 

try it

[ohm_question]146079[/ohm_question]  
   

Exercises

Subtract: [latex]\left({m}^{2}-3m+8\right)[/latex] from [latex]\left(9{m}^{2}-7m+4\right)[/latex].

Answer: Solution

Subtract: [latex]\left({m}^{2}-3m+8\right)[/latex] from [latex]\left(9{m}^{2}-7m+4\right)[/latex].
Distribute and identify like terms. .
Rearrange the terms. .
Combine like terms. [latex]8m^2-4m-4[/latex]

 

TRY IT

[ohm_question]146085[/ohm_question]
In the next video we show more examples of adding and subtracting polynomials. https://youtu.be/jiq3toC7wGM

Licenses & Attributions

CC licensed content, Original

  • Question ID 146085, 146084, 146078, 146070, 146073. Authored by: Lumen Learning. License: CC BY: Attribution.

CC licensed content, Shared previously

  • Ex: Adding Polynomials. Authored by: James Sousa (mathispower4u.com). License: CC BY: Attribution.
  • Ex: Adding and Subtracting Polynomials. Authored by: James Sousa (mathispower4u.com). License: CC BY: Attribution.

CC licensed content, Specific attribution