🎓 Mathematics • Algebra
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Algebra Calculator
Solves algebraic expressions, evaluates polynomials at real values, expands binomials, and differentiates.
Algebra & Matrix Engine
Algebra & Matrix Studio
Solve quadratic equations with complex roots, 2x2 systems via Cramer's rule, binomial FOIL expansions, and 2x2/3x3 matrix linear algebra with instant proofs.
Algebra Mode
Expand binomial product: (a₁x + b₁)(a₂x + b₂)
Binomial 1 (a₁x + b₁)
Binomial 2 (a₂x + b₂)
Expanded Quadratic Form
(2x + 3)(1x - 4)
= 2x² - 5x - 12
FOIL Breakdown (First, Outer, Inner, Last)
F (First):First: (2x) × (1x) = 2x²
O (Outer):Outer: (2x) × (-4) = -8x
I (Inner):Inner: (3) × (1x) = 3x
L (Last):Last: (3) × (-4) = -12
What is Algebra?
Algebra represents relationships between variables using symbols, letters, and operations.
Polynomial evaluation, binomial expansion, and factoring form the basis for calculus and computer science.
Formula & Step-by-Step Calculation
P(x) = ax² + bx + c
Evaluates standard quadratic and higher polynomial forms.
Worked Step-by-Step Examples
Example 1
Expand (x + 2)(x + 3)
Solution: x² + 5x + 6
• x·x + 3x + 2x + 6 = x² + 5x + 6
Common Real-World & Academic Use Cases
- ✓ Algebra homework
- ✓ Engineering trajectory formulas
- ✓ Curve analysis
How to Use the Algebra Calculator
1
Select Operation
Choose evaluation or expansion.
2
Input Coefficients
Fill in numbers.
3
Review Solution
Read expanded expression.
Frequently Asked Questions
Q: What is FOIL?
First, Outer, Inner, Last method for binomial multiplication.