Section 7.2: Adding & Subtracting Polynomials
To add or subtract polynomials, combine like terms—terms with the same variable raised to the same power.
Example 1
Add: \( (3x^2 + 5x - 2) + (x^2 - 3x + 7) \)
Combine like terms:
\( (3x^2 + x^2) + (5x - 3x) + (-2 + 7) = 4x^2 + 2x + 5 \)
Example 2
Subtract: \( (5y^3 - 2y + 1) - (3y^3 + y - 4) \)
Distribute the negative sign and combine like terms:
\( 5y^3 - 2y + 1 - 3y^3 - y + 4 = 2y^3 - 3y + 5 \)
Practice Problems
- \( (2x^2 + 3x + 4) + (x^2 - x + 5) \)
- \( (4y^3 - y + 2) - (2y^3 + 3y - 1) \)
- \( (x^4 + 2x^3 - x) + (3x^4 - x^3 + 5x) \)
- \( (5a^2 - 3a + 7) - (2a^2 + 4a - 1) \)
- \( (x^2 + x + 1) + (x^2 - x + 4) \)