Subtracting polynomials is understood as adding the additive inverse of the subtrahend: every term in the polynomial being subtracted changes sign, and only like terms—those with identical variable parts and exponents—are combined by adding their coefficients. This includes simplifying one-variable polynomials with integer or rational coefficients and whole-number exponents, supporting later work with equations and functions; polynomial division, multivariable generalizations, and abstract polynomial theory are outside this scope.
To subtract polynomials, change the sign of every term in the polynomial being subtracted. Then combine like terms.
Example:
Step 1: Change the signs in the second polynomial.
The subtraction sign applies to every term:
Step 2: Group like terms.
Like terms have the same variable and exponent:
Step 3: Combine the coefficients.
Therefore,
Remember: only combine like terms, such as with and with .
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