Subtract Polynomials

Subtracting polynomials

To subtract polynomials, distribute the minus sign across the entire second polynomial, then combine like terms.

Step-by-step method

1. Rewrite the expression so the subtraction is clear.
2. Change the signs of every term in the polynomial being subtracted. For example, subtracting ((3x^2 - 4x + 1)) means adding ((-3x^2 + 4x - 1)).
3. Remove parentheses carefully.
4. Combine like terms: match powers of the same variable and constants.
5. Write the result in simplified form, usually with terms ordered from highest to lowest degree.

Example structure

If you have [ (5x^2 + 2x - 7) - (3x^2 - 4x + 1), ] first distribute the minus sign: [ 5x^2 + 2x - 7 - 3x^2 + 4x - 1. ] Then combine like terms: [ (5x^2 - 3x^2) + (2x + 4x) + (-7 - 1) = 2x^2 + 6x - 8. ]

Check your work

A good check is to make sure every term in the second polynomial changed sign before combining. Then verify that no like terms are left uncombined and that the final expression is simplified.