While addition and subtraction of polynomials, we simply add or subtract the terms of the same power. The power of variables in a polynomial is always a whole number, power can not be negative, irrational, or a fraction. It is straightforward to add or subtract two polynomials. A polynomial is a mathematics expression written in the form of a_{0}X^{n} + a_{1}x^{n−1} + a_{2}x^{n−2} + ...... + a_{n}X^{0}.
The above expression is also called polynomial in standard form, where a_{0}, a_{1}, a_{2} ......... a_{n} are constants, and n is a whole number. For example x^{2} + 2x + 3, 5x^{4 } 4x^{2} + 3x + 1 and 7x  √3 are polynomials.
The addition of polynomials is simple. While adding polynomials, we simply add like terms. We can use columns to match the correct terms together in a complicated sum. Keep two rules in mind while performing the addition of polynomials.
The subtraction of polynomials is as simple as the addition of polynomials. Using columns would help us to match the correct terms together in a complicated subtraction. While subtracting polynomials, separate the like terms and simply subtract them. Keep two rules in mind while performing the subtraction of polynomials.
The addition or subtraction of polynomials is very simple to perform, all we need to do is to keep some steps in mind. To perform the addition and subtraction operation on the polynomials, the polynomials can be arranged vertically for complex expressions. For simpler calculations, we can perform the operation using the horizontal arrangement.
Polynomials can be added and subtracted in horizontal arrangement using the steps given below,
Polynomials can be added and subtracted in vertical arrangement using the steps given below,
By following these steps we can solve adding and subtracting polynomials.
Example: (3x^{3} + x^{2}  2x 1) + (x^{3} + 6x + 3).
The given polynomials are arranged in their standard forms.
Addition performed horizontally:
Addition performed vertically:
Important Notes
 The highest power of the variable in a polynomial is called the degree of the polynomial.
 The algebraic expressions having negative or irrational power of the variable are not polynomials.
 Addition and subtraction in polynomials can only be performable on like terms.
Example: Add two polynomials, 3x + 2y, and 4y + 5z to find the solution.
Solution: Given polynomials are (3x + 2y) + (4y + 5z). Here like terms are only 2y and 4y.
So addition can only be performed on these two terms, the other terms 3x and 5z will not get affected.
3x + (2y + 4y) + 5z
= 3x + (2 + 4)y + 5z
= 3x + 6y + 5z
Therefore, answer is 3x + 6y + 5z.
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