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.

Examples

Example 1

Mark and simplify the sum of polynomials [[$ 2a+3 $]] and [[$ -5a+1 $]].

The sum is marked [[$ (2a+3)+(-5a+1) $]].

Example 2

Mark and simplify the opposite polynomial of [[$ -6a^2+b-1 $]].

The opposite polynomial is formed by placing a minus sign in front of the polynomial.

Example 3

Mark and simplify the difference of polynomials[[$ 2a+3 $]] and [[$ -5a+1 $]].

The polynomials are subtracted from one another by adding the opposite polynomial of the latter polynomial to the first polynomial.

Example 4

Calculate the value of polynomial [[$ a-3a^2+4-5a-(3-2a^2-4a) $]] when[[$ a=10 $]].

Before placing the value of a variable inside the expression, you should simplify the polynomial!

[[$ a-3a^2+4-5a-(3-2a^2-4a) = a-3a^2+4-5a-3+2a^2+4a =-a^2+1 $]]

Place 10 in the place of a in the simplified expression [[$ -a^2+1 $]].

[[$ -10^2+1=-100+1=-99 $]]