Addition and Subtraction

4-2Adding and Subtracting Polynomials

Overview

Combine like terms (same variable, same exponent). Watch signs when subtracting.

Key ideas

  • Like terms have identical variable parts.
  • Subtraction distributes a negative sign to every term.
  • Arrange by descending powers for clarity.

Worked examples

Example 1

Problem. Add (3x^2 + 2x − 1) + (x^2 − 5x + 4).

Solution. 4x^2 − 3x + 3

Example 2

Problem. Subtract (5y − 3) − (2y + 7).

Solution. 3y − 10

Practice

Try each one. Click Show answer when ready.

  1. 1.

    (2x + 5) + (3x − 8)

  2. 2.

    (x^2 − 4) − (x^2 + 6)

  3. 3.

    (4a^2 + a) + (a^2 − 3a + 2)

Challenge problems

A little tougher — great for test prep. Click Show answer when ready.

  1. 1.

    Simplify (5x² − 3x + 7) − (2x² + 5x − 3).

  2. 2.

    Simplify 3(2a² + a − 4) + 2(−a² + 3a + 5).