Symbolic Algebra

Polynomials, partial fractions, series, and trig identities.

Parameters

Polynomial P(x) coeffs

Poly Arithmetic

P(x) coeffs Q(x) coeffs

Examples

Function

Terms N 5

Expand around a

LHS expression (use x) RHS expression

Presets

Live Data

See Live Data panel for step-by-step partial fraction decomposition.

Pythagorean Identities

sin²x+cos²x=1
tan²x+1=sec²x
1+cot²x=csc²x

Double Angle

sin(2x)=2sin(x)cos(x)
cos(2x)=cos²x−sin²x
tan(2x)=2tan(x)/(1−tan²x)

Sum-to-Product

sin(A)+sin(B)=2sin(½(A+B))cos(½(A−B))
cos(A)+cos(B)=2cos(½(A+B))cos(½(A−B))

Computer Algebra & Symbolic Math Handbook

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.