Subtraction of Polynomials

Subtraction of polynomials is a similar process to adding polynomials, with the main difference being the handling of negative signs. When subtracting polynomials, we need to carefully change the signs of the terms being subtracted before combining like terms.

There are two common methods for subtracting polynomials:

• Row Method

• Column Method

• Enclose the subtracted expression in brackets and prefix it with a minus sign.

• Remove the brackets by changing the sign of each term inside the bracket.

• Combine the like terms

• Rewrite the expressions in two rows (lines), placing the terms of the expression to be subtracted in the second row and aligning like terms vertically.

• Change the signs of each term in the lower row (subtracting the terms).

• Add column-wise

Subtract 3a − 4b + 5c from 4a − b + 6c. 
Solution:

4a − b + 6c − (3a − 4b + 5c)  [Step 1.]

= 4a − b + 6c − 3a + 4b − 5c  [Step 2]

= 4a − 3a − b + 4b + 6c − 5c [Step 3]

= a + 3b + c

5x² − 7x + 4 and −3x² + 5x + 2, subtract x² + x + 1. 
Solution:

(5x² − 7x + 4) + (−3x² + 5x + 2) −  (x² + x + 1)

= 5x² − 7x + 4 - 3x² + 5x + 2 - x² − x − 1

= 5x² − 3x² − x² − 7x + 5x − x + 4 + 2 − 1

= 5x² − 4x² − 8x + 5x + 6 − 1

= x² − 3x + 5 

Subtract 3a − 4b + 5c from 4a − b + 6c. 

Step 1:   4a − b  + 6c
              3a − 4b + 5c
Step 2: −     +     −         
Step 3:  a  +  3b  +  c 

5x² − 7x + 4 and −3x² + 5x + 2, subtract x² + x + 1.

   5x² − 7x + 4
− 3x² + 5x + 2            Add
   2x² − 2x + 6
      x² + x + 1
−       −      −     
    x² − 3x + 5            Subtract       

• Always flip signs when removing brackets preceded by a minus.

• Align like terms in columns for neat addition.

• Check your work by reversing the subtraction as addition of the opposite.