Examples
Example 1
Mark and simplify the sum of polynomials [[$ 2a+3 $]] and [[$ -5a+1 $]].
The sum is marked [[$ (2a+3)+(-5a+1) $]].![A plus sign before brackets does not change the signs of the terms inside the brackets.](https://peda.net/qis/2022-2023/mathematics/ematematiikka-722/oipjp/1pyjv/esimerkkej%C3%A4/7:file/photo/a4e4624d1c3e09f508135abb5b05bbdc9e4cccb8/13_example1.png)
Example 2
Mark and simplify the opposite polynomial of [[$ -6a^2+b-1 $]].
The opposite polynomial is formed by placing a minus sign in front of the polynomial.
![Remember to place a polynom in brackets so that the minus sign affects all of the terms inside them. Because there is a minus sign before the brackets, the signs of all terms inside the brackets must be changed.](https://peda.net/qis/2022-2023/mathematics/ematematiikka-722/oipjp/1pyjv/esimerkkej%C3%A4/72:file/photo/e175498a8160357db3357f5915594f51afee720d/13_example2.png)
Example 3
Mark and simplify the difference of polynomials[[$ 2a+3 $]] and [[$ -5a+1 $]].
The polynomials are subtracted from one another by adding the opposite polynomial of the latter polynomial to the first polynomial.
![Because there is a minus sign before the brackets, the signs of all terms inside the brackets must be changed.](https://peda.net/qis/2022-2023/mathematics/ematematiikka-722/oipjp/1pyjv/esimerkkej%C3%A4/73:file/photo/0912c250e998a0d86d1eb96c9e9d8c569ba05207/13_example3.png)
Example 4
Calculate the value of polynomial [[$ 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 $]]