Math A

Subtracting
Polynomials

 

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)

(Change the signs of terms being subtracted)

= (2x2 - 4) + (-x2 - 3x + 3) 

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

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

= x2 - 3x - 1

 

2. Using the vertical method to subtract like terms:
 

        2x² + 0x - 4
       -(x²+ 3x - 3)
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    2x²+ 0x - 4
    -x²- 3x + 3 (signs changed)
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     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 using the distributive property.

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

 

 

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Roberts

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