Algebra 101 - Unit 5

Lesson 25: Adding and Subtracting Polynomials

Adding and subtracting polynomials involves combining like terms. Like terms are terms that have the same variable raised to the same power.

Steps for Adding Polynomials

1. Arrange the polynomials in standard form (optional, but helps clarity).
2. Combine like terms by adding their coefficients.
3. Write the result in standard form, if desired.

Steps for Subtracting Polynomials

1. Distribute the negative sign to all terms of the polynomial being subtracted.
2. Combine like terms by adding coefficients.
3. Write the result in standard form.

Examples

Example 1 — Adding Polynomials:

(3x² + 5x − 2) + (4x² − 3x + 6)

Combine like terms:

3x² + 4x² = 7x², 5x − 3x = 2x, −2 + 6 = 4

Answer: 7x² + 2x + 4

Example 2 — Subtracting Polynomials:

(5x³ + 2x − 7) − (3x³ − x + 4)

Distribute the negative: 5x³ + 2x − 7 − 3x³ + x − 4

Combine like terms: 5x³ − 3x³ = 2x³, 2x + x = 3x, −7 − 4 = −11

Answer: 2x³ + 3x − 11

Practice Problems

1. (2x² + 3x + 5) + (x² − x + 4)
2. (4x³ − 2x + 7) − (x³ + x − 3)
3. (5x² − 3x + 1) + (−2x² + 4x − 6)
4. (3x³ + 2x² − x + 5) − (2x³ − x² + 4x − 2)