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Guide allo studio > 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: 17x2+6x217{x}^{2}+6{x}^{2}. Solution
17x2+6x217{x}^{2}+6{x}^{2}
Combine like terms. 23x223{x}^{2}
 

try it

[ohm_question]146075[/ohm_question]
   

example

Subtract: 11n−(−8n)11n-\left(-8n\right).

Answer: Solution

11n−(−8n)11n-\left(-8n\right)
Combine like terms. 19n19n

 

try it

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

example

Simplify: a2+4b2−7a2{a}^{2}+4{b}^{2}-7{a}^{2}.

Answer: Solution

a2+4b2−7a2{a}^{2}+4{b}^{2}-7{a}^{2}
Combine like terms. −6a2+4b2-6{a}^{{}^{2}}+4{b}^{2}
Remember, −6a2-6{a}^{2} and 4b24{b}^{2} 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: (4x2−5x+1)+(3x2−8x−9)\left(4{x}^{2}-5x+1\right)+\left(3{x}^{2}-8x - 9\right).

Answer: Solution

(4x2−5x+1)+(3x2−8x−9)\left(4{x}^{2}-5x+1\right)+\left(3{x}^{2}-8x - 9\right)
Identify like terms. .
Rearrange to get the like terms together. .
Combine like terms. 7x2−13x−87x^2-13x-8

 

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: (7u2−5u+3)−(4u2−2)\left(7{u}^{2}-5u+3\right)-\left(4{u}^{2}-2\right).

Answer: Solution

(7u2−5u+3)−(4u2−2)\left(7{u}^{2}-5u+3\right)-\left(4{u}^{2}-2\right)
Distribute and identify like terms. .
Rearrange the terms. .
Combine like terms. 3u2−5u+53{u}^{2}-5u+5

 

try it

[ohm_question]146079[/ohm_question]  
   

Exercises

Subtract: (m2−3m+8)\left({m}^{2}-3m+8\right) from (9m2−7m+4)\left(9{m}^{2}-7m+4\right).

Answer: Solution

Subtract: (m2−3m+8)\left({m}^{2}-3m+8\right) from (9m2−7m+4)\left(9{m}^{2}-7m+4\right).
Distribute and identify like terms. .
Rearrange the terms. .
Combine like terms. 8m2−4m−48m^2-4m-4

 

TRY IT

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

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