Adding and Subtracting Polynomials are the operations performed on a polynomial.
Adding and subtracting are two of the most basic operations you have. When solving equations with variables on each side, you have been able to
rearrange all variables to be on one side of the equation by adding or subtracting all the monomials on a selected side of the equation.
To simplify an equation, you have combined like variables by adding or subtracting terms with the same variable and exponents.
What are polynomials?
Polynomials are mathematical expressions that contain multiple terms. Basic operations such as addition, subtraction, multiplication, and division can be used to combine or simplify polynomials.
Adding and subtracting polynomials involves combining like terms, which are those with the same variables and exponents.
Steps to add or subtract polynomial
Step 1: Put the polynomials into standard form
To add or subtract polynomials, the first step is to put both polynomials in their standard form. In the following example, we have accomplished that step:
(-17x^3 + 8x^2 – 20x + 5) + (20x^3 – 4x^2 + 32x – 3)
Step 2: Arrange the like terms in columns and add as usual
Step 1: Arrange Polynomials
Both polynomials must be arranged in their standard form, which we have accomplished in this example,
(14z3 – 12z2 + 15z – 3) – (7z3 + 3z2 – 10z + 5)
Step 2: Change the sign of subtracting terms and arrange them and subtract
Since the entire second polynomial is subtracted, the sign of each term in the second polynomial can be changed so that all positive terms become negative terms and all negative terms become positive terms. Thus, we have
(14z^3 – 12z^2 + 15z – 3)- 7z^3 – 3z^2 + 10z – 5
Thus, the result is 7z^3 – 15z^2 + 25z – 8.
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