Subtracting Polynomials
When we subtract polynomials, we subtract the like terms. Because a  b = a +
(b), we can subtract by adding the opposite of the second polynomial to the
first polynomial. Remember that a negative sign in fron of parentheses changes
the sign of each term in the parentheses. For example,
(x^{2}  2x + 8) = x^{2} + 2x  8.
Polynomials can be subtracted horizontally or vertically, as shown in the
next example.
Subtracting polynomials
Perform the indicated operation.
a) (x^{2}  5x  3)  (4x^{2} + 8x  9)
b) (4y^{3}  3y + 2)  (5y^{2} 7y  6)
Solution
a) (x^{2}  5x  3)  (4x^{2} + 8x  9) 
= x^{2}  5x  3  4x^{2}  8x + 9 
Change signs. 

= 3x^{2}  13x + 6 
Add. 
b) To subtract 5y^{2}  7y 6 from 4y^{3}  3y + 2 vertically,
we line up the like terms as we do for addition:
4y^{3} 

 3y 
+ 2 
 
(5y^{2} 
 7y 
 6) 
Now change the signs of 5y^{2}  7y  6 and add the like terms:
4y^{3} 

 3y 
+ 2 

5y^{2} 
+
7y 
+
6) 
4y^{3} 
5y^{2} 
+ 4y 
+ 8 
Caution
when adding or subtracting polynomials vertically, be sure to line up the
like terms.
