Algebraïsche Identiteiten
Begrijpen en toepassen van algebraïsche identiteiten
Interactive Algebraic Identities Visualization
Introduction
Algebraic identities are mathematical equations that are true for all values of the variables involved. They are fundamental tools in algebra for simplifying expressions, solving equations, and factoring polynomials.
Key Concepts:
- Identity: An equation that holds true for all variable values
- Expansion: Breaking down expressions into simpler terms
- Factorization: Writing expressions as products of factors
- Verification: Checking that both sides of an identity are equal
- Application: Using identities to simplify complex algebraic expressions
How to Use
- Select an algebraic identity from the dropdown to explore different formulas
- Adjust the values of a, b, and c (if needed) using the sliders
- Watch the verification panel to see both sides of the identity calculated
- Enable "Show Step-by-Step Expansion" to see how the identity is derived
- Try different values to verify that the identity holds for all numbers
- Use these identities to simplify complex algebraic expressions in your calculations
Identity
(a + b)² = a² + 2ab + b²
Square of the sum of two terms
Verification
Step-by-Step Expansion
Step 1: (a + b)² = (a + b)(a + b)
Step 2: = a(a + b) + b(a + b)
Step 3: = a² + ab + ab + b²
Step 4: = a² + 2ab + b²
Applications of Algebraic Identities
1. Simplifying Expressions:
Use identities to expand or factor expressions quickly without manual multiplication.
2. Solving Equations:
Factor equations using identities to find solutions more easily.
3. Mental Math:
Calculate squares and cubes of numbers mentally using these identities.
4. Proofs:
Use identities to prove other mathematical statements and theorems.
Lessen
Individuele leereenheden
Lessen komen binnenkort