Combining Polynomials in 2026 Algebra
Polynomial addition and subtraction rely on the Distributive Property in reverse: combining "like terms"—terms containing identical variable bases raised to identical exponents.
When subtracting polynomials, the negative sign must be distributed to every term inside the second parentheses before grouping like terms.
Like Terms Classification Reference Table
| Algebraic Term 1 | Algebraic Term 2 | Like Terms? | Combined Sum |
|---|---|---|---|
| $4x^2$ | $-7x^2$ | Yes (Same variable and power) | $-3x^2$ |
| $5x$ | $8x$ | Yes (Linear terms) | $13x$ |
| $3x^2$ | $3x$ | No (Different exponents) | Cannot combine ($3x^2 + 3x$) |
| $6xy$ | $-2yx$ | Yes (Commutative multiplication) | $4xy$ |
Mathematical Formulations
(a_1 x^2 + b_1 x + c_1) \pm (a_2 x^2 + b_2 x + c_2) = (a_1 \pm a_2)x^2 + (b_1 \pm b_2)x + (c_1 \pm c_2)