Exponent Operations Calculator (Add/Sub)
Simplify algebraic expressions involving addition and subtraction of exponents. Identify like terms and avoid common factorization errors.
About
Algebraic simplification often trips up students when distinguishing between multiplication and addition rules. While multiplying exponents involves adding powers, adding exponents requires strict adherence to the "Like Terms" rule. This tool specifically targets the simplification of polynomial expressions where terms are added or subtracted. It identifies common bases and exponents to factor expressions correctly, preventing the frequent error of combining unlike terms such as x2 + x3 into x5.
Accuracy in these operations is fundamental for calculus and engineering physics, where correct coefficient manipulation determines the integrity of differential equations. This utility enforces the logic that only terms with identical variable parts can be merged.
Formulas
The fundamental rule for adding or subtracting terms with exponents is the Distributive Property of Multiplication over Addition. You can only combine terms if both the base and the exponent are identical.
If the terms are not "like terms," the expression remains a polynomial sum rather than a single monomial.
Reference Data
| Operation Type | Expression | Correct Result | Common Error (Trap) |
|---|---|---|---|
| Like Terms Addition | x2 + x2 | 2x2 | x4 |
| Unlike Terms | x2 + x3 | x2 + x3 | x5 |
| Subtraction | 5y4 − 2y4 | 3y4 | 3 |
| Multiplication (Contrast) | x2 ⋅ x3 | x5 | x6 |
| Zero Exponent | x0 + x0 | 2 | x |
| Negative Coefficients | −x2 − x2 | −2x2 | 0 |
| Variable Mismatch | x2 + y2 | x2 + y2 | (xy)2 |
| Coefficient Grouping | axn + bxn | (a+b)xn | abx2n |