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.
(2x + 5) + (3x − 8)
- 2.
(x^2 − 4) − (x^2 + 6)
- 3.
(4a^2 + a) + (a^2 − 3a + 2)
Challenge problems
A little tougher — great for test prep. Click Show answer when ready.
- 1.
Simplify (5x² − 3x + 7) − (2x² + 5x − 3).
- 2.
Simplify 3(2a² + a − 4) + 2(−a² + 3a + 5).