Matematicas
Calculadora verificada con fórmula transparente
Difference of Squares Calculator.
Calculates the difference between two squares and shows the factored form (a² - b² = (a + b)(a - b)).
Tus entradas
Cómo funciona
- 1
Enter the values for a and b.
- 2
Square each value: a² and b².
- 3
Subtract b² from a² to get the difference.
- 4
The factored form is (a + b)(a - b), which equals the same result.
a^2 - b^2Preguntas frecuentes
What is the difference of squares formula?
The formula is a² - b² = (a + b)(a - b). It shows that the difference of two squares can be factored into the product of their sum and difference.
Can a and b be negative?
Yes, the formula works for any real numbers. For example, (-7)² - 2² = 49 - 4 = 45, and (-7 + 2)(-7 - 2) = (-5)(-9) = 45.
What if a equals b?
If a = b, then a² - b² = 0, and the factored form (a + b)(a - b) also equals 0 because (a - b) = 0.
Explorar esta categoría de calculadoras
Resultados
Fórmula verificadaEstimación solo como guía general: verifica decisiones importantes con un profesional adecuado.
Cómo funciona
Calculates the difference between two squares and shows the factored form (a² - b² = (a + b)(a - b)).
- Enter the values for a and b.
- Square each value: a² and b².
- Subtract b² from a² to get the difference.
- The factored form is (a + b)(a - b), which equals the same result.
Fórmulas
Las matemáticas detrás de esta calculadora, escritas para que puedas verificar el resultado.
Difference of Squares
This identity states that the difference between two squares equals the product of the sum and difference of the two numbers.
Example:
Input: a = 5, b = 3
Calculation: 5² - 3² = 25 - 9 = 16, and (5+3)(5-3) = 8 × 2 = 16
Result: 16
Casos de uso reales
Dónde aparece este cálculo en la vida cotidiana.
Simplifying algebraic expressions
Factor expressions like x² - 9 quickly into (x + 3)(x - 3).
Example: x² - 9 = (x + 3)(x - 3)
Mental math
Compute differences of squares without a calculator, e.g., 99² - 1² = (99+1)(99-1) = 100 × 98 = 9800.
Example: 99² - 1² = 9800
Solving equations
Use the identity to solve quadratic equations that are in the form a² = b².
Example: x² = 16 → x² - 16 = 0 → (x+4)(x-4)=0 → x = ±4
Consejos y errores comunes
Tips
- Remember the identity: a² - b² = (a + b)(a - b).
- Check your result by expanding (a + b)(a - b) to see if you get a² - b².
- The formula works for any real numbers, including fractions and decimals.
- Use the factored form to simplify calculations when a and b are large.
Common Mistakes to Avoid
- Forgetting that a² - b² is not equal to (a - b)². (a - b)² = a² - 2ab + b².
- Confusing the order: a² - b² is not the same as b² - a² unless you factor out a negative.
- When a and b are negative, forgetting that squaring makes them positive.
Supuestos y limitaciones
- Use the stated inputs and units.
- Results are estimates for planning and education.
- Check measurements and source data before making an important decision.