Polynomials are mathematical expressions formed by monomials, that is, by algebraic terms composed of numbers, variables or a multiplication between numbers and variables.
At addition and subtraction of polynomials, it is important to understand the concept of similar algebraic terms.
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Similar algebraic terms or similar monomials are those that have the same literal part, that is, the part formed by variables is equal.
Consider, for example, the algebraic terms 3abc, 4a²b, and 2abc. Among them, only 3abc and 2abc are similar, as in both the literal part is abc.
At addition of polynomials, we operate only with the coefficients of the similar algebraic terms and keep, in the expression, the terms that are not similar.
Example:
Perform the addition of polynomials It is
.
First, let's write the polynomials in parentheses, with the plus sign between them.
Then we remove the parentheses, making the sign game:
Now, we perform the operations between the coefficients of like terms:
At polynomial subtraction, we also operate only with the coefficients of the similar algebraic terms and keep, in the expression, the terms that are not similar.
Example:
Perform the subtraction of polynomials It is
.
First, let's write the polynomials in parentheses, with the minus sign between them.
So, we eliminate the parentheses, making the sign game:
Now, we perform the operations between the coefficients of like terms:
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