To add and subtract polynomials, you need to combine like terms. Like terms are terms that have the same variable raised to the same power.
Example of adding polynomials:
(2x^2 + 4x + 5) + (3x^2 - 2x + 9)
First, you need to group the like terms together:
(2x^2 + 3x^2) + (4x - 2x) + (5 + 9)
Then, you can simplify by adding the coefficients:
5x^2 + 2x + 14
Therefore, the sum of (2x^2 + 4x + 5) and (3x^2 - 2x + 9) is 5x^2 + 2x + 14.
Example of subtracting polynomials:
(4x^2 - 6x + 9) - (2x^2 + 3x - 1)
First, you need to distribute the negative sign:
4x^2 - 6x + 9 - 2x^2 - 3x + 1
Then, you need to group the like terms together:
(4x^2 - 2x^2) + (-6x - 3x) + (9 + 1)
Next, you can simplify by adding the coefficients:
2x^2 - 9x + 10
Therefore, the difference of (4x^2 - 6x + 9) and (2x^2 + 3x - 1) is 2x^2 - 9x + 10.