1Cademy - Adding and Subtracting Polynomials

Learn Before

Polynomial

Concept

Adding and Subtracting Polynomials

Adding and subtracting polynomials amounts to adding and subtracting the individual monomials that compose each polynomial. Since a polynomial is built from monomials joined by addition or subtraction, combining two polynomials simply merges all of their terms into one expression. To simplify the result, identify the like terms — those sharing the same variable(s) raised to the same exponent(s) — and use the Commutative Property of Addition to rearrange the expression so that like terms sit next to each other. Then combine like terms by adding or subtracting their coefficients while keeping the variable part unchanged.

When adding polynomials, the terms from both polynomials are brought together directly and like terms are combined.

When subtracting one polynomial from another, first distribute the subtraction across the second polynomial by changing the sign of every term in it (equivalent to multiplying each term by $-1$ ). After the signs have been changed, the problem reduces to adding like terms, just as in polynomial addition.

Updated 2026-05-13

Contributors are:

Who are from:

References

Learn Before

Related

Learn After