Subtracting Polynomials
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Alph0023.gif (2254 bytes)ubtract like terms by changing the signs of the terms being subtracted, and following the rules for adding polynomials.

 

Example:  Simplify:  (2x2 - 4) - (x2 + 3x - 3)

Below are several different ways to attack this example:

 1. Using a horizontal method to subtract like terms:

Change the signs of ALL of the terms being subtracted.  Change the subtraction sign to addition.  Follow the rules for adding signed numbers.

 

(2x2 - 4) - (x2 + 3x - 3)

  
 

= (2x2 - 4) + (-x2 - 3x + 3)

... change signs of terms being subtracted and change subtraction to addition.
 

= 2x2 - 4 + -x2 - 3x + 3

 ... identify like terms
 

= 2x2 - x2 - 3x - 4 + 3

 ... group the like terms
 

= x2 - 3x - 1

 ... add the like terms

 

2. Using the vertical method to subtract like terms:
 

        2x² + 0x - 4
       -(x²+ 3x - 3)
Line.gif (926 bytes)
Now, change signs of all terms being
subtracted and follow rules for add.

    2x² + 0x  - 4
    -x²  -  3x + 3 (signs changed)
Line.gif (926 bytes)
     x²  -  3x  - 1

 

 3.  Using algebra tiles to subtract like terms:
Key: Sp_sub16.jpg = x² Sp_sub17.jpg = -x² Sp_sub18.jpg

(2x2 - 4) - (x2 + 3x - 3)

The diagram below shows the signs 
changed to  -x2 - 3x + 3 and  addition occurring.

Sp_sub19.jpg

 

4.  Using the Distributive Property to subtract like terms:  
When you are subtracting the coefficients (the numbers in front of the variables) of like terms, you are actually using the distributive property in reverse.

4x2 - 5x2 = (4 - 5) x2 = -x2