Adding and Subtracting Polynomials

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.

Students from Rio de Janeiro will compete for medals at the Olympics…

The Institute of Mathematics is open for registration for the Olympics…

Similar algebraic terms

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.

addition of polynomials

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 $\dpi{120} \mathrm{x^2 - 8x + 9}$ It is $\dpi{120} \mathrm{3x^2 + 4x- 5}$ .

First, let's write the polynomials in parentheses, with the plus sign between them.

$\dpi{120} \mathrm{(x^2 - 8x + 9) +(3x^2 + 4x -5)}$

Then we remove the parentheses, making the sign game:

$\dpi{120} \mathrm{x^2 - 8x + 9 +3x^2 + 4x -5}$

Now, we perform the operations between the coefficients of like terms:

$\dpi{120} \mathrm{4x^2 - 4x + 4 }$

subtraction of polynomials

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 $\dpi{120} \mathrm{7x + 3y - 6xy}$ It is $\dpi{120} \mathrm{-2x + 3xy +5y}$ .