While using the column method for subtraction of polynomials, the expression that is being subtracted from is written on top and the expression that is to be subtracted is written underneath it such that the like terms are in the same column. Then, change the sign of all the terms of the expression written in the below row.
For example,
Subtract (3y + 4 – 12xy + x) from (21xy + 18 – 7x + y)
Write (21xy + 18 – 7x + y) on top and (3y + 4 – 12xy + x) underneath. 21xy + 18 – 7x + y
– 12xy + 4 + x + 3y
Changing the sign of all the terms of the expression written in the below row, 21xy + 18 – 7x + y
+ 12xy – 4 – x – 3y
Now, solving the like terms in the columns,
21xy + 18 – 7x + y
+ 12xy – 4 – x – 3y
———————-
33xy + 14 – 8x – 2y
Thus, (21xy + 18 – 7x + y) – (3y + 4 – 12xy + x) = 33xy – 8x – 2y + 14.