Symbolic Algebra

Mathematical Principles & Theorems

Employs symbolic computation and Computer Algebra System (CAS) term-rewriting: Exact arithmetic (avoiding floating-point rounding errors), symbolic differentiation \(\frac{d}{dx}[f(x)]\), polynomial expansion \((x+a)(x+b) = x^2 + (a+b)x + ab\), algebraic factoring, rational expression simplification, trigonometric identity substitution via Euler formulas \(\cos x = \frac{e^{ix}+e^{-ix}}{2}\), and formal Taylor series expansions.

Operating Instructions

• Enter an algebraic expression in the mathematical input field.
• Select symbolic CAS operation: Simplify, Expand, Factor, Differentiate, or Taylor Series.
• For Taylor series: Set expansion order \(N\) using the precise numeric value box.
• Click Compute to view the exact symbolic transformation rendered in formatted mathematical typography.