Adding and subtracting polynomials
You must pay attention to the addition and subtraction of polynomials when removing brackets from expressions. The plus sign in front of the brackets does not change the signs of the terms when the brackets are removed. If there is a minus sign in front of the brackets, the signs of all terms must be reversed when removing the brackets. If you do not remember how to replace combinations of two signs and numbers with one character, recall them from the following table.
| The combination of sign | Replaced by | Example |
|---|---|---|
| [[$ +(+ $]] | [[$ + $]] | [[$ +(+2) = 2 $]] |
| [[$ -(+ $]] | [[$ - $]] | [[$ -(+2) = -2 $]] |
| [[$ +(- $]] | [[$ - $]] | [[$ +(-2) = -2 $]] |
| [[$ -(- $]] | [[$ + $]] | [[$ -(-2) = 2 $]] |
When two polynomials that are added together result in a sum of zero, they are said to be one another's opposite polynomials.
The opposite polynomial of a polynomial is obtained by changing the sign of each term in the polynomial.