Polynomials:
Polynomials are algebraic expressions consisting of one or more terms connected by addition or subtraction signs. They can be classified by the number of terms. If there is one term it is called a monomial. If there are two terms the polynomial is called a binomial. If there are three terms the polynomial is called a trinomial. However if there is more than three terms in the polynomial, it is classified as a polynomial.
Like Terms:
Like terms are terms that have the same variable raised to the same exponent.
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All of these terms are like terms because they all have the same variable raised to the same exponent. For terms to be like terms they don't need to have the same coefficient.
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These terms are not like terms because they have different the first term, 7y, doesn't have the same variable as the other terms. The second term, y^3, isn't a like term with 8xy^3 because it doesn't have one of the variables (x).
Adding and Subtracting Polynomials:
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To add or subtract polynomials, you first need to collect like terms. To collect like terms you need to re-write the question. When re-writing the question, make sure to bring the sign of the term when re-writing meaning if there is a negative in front of the term, you need to write it in with the term.
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In the next step you can see that the person collected like terms carrying the signs in front of the term. The next step is to add or subtract the coefficient. When adding or subtracting make sure that you don't change the variables of the exponents. Also remember that if there is no written coefficient on the variable, that there is always a one (1) in front of it. Remember that exponent rules are only used for multiplication and division, not addition and subtraction.
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After completing all of the steps, you will be left with your final answer!