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Test de igualdad e identidad algebraica

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Test de igualdad e identidad algebraica

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Preguntas sobre identidades y equalidades

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Jonathan Gonzalez
Jonathan Gonzalez
Mexico

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Test de igualdad e identidad algebraica
 

Test de igualdad e identidad algebraicaOnline version

Preguntas sobre identidades y equalidades

by Jonathan Gonzalez
1

La igualdad (a+b)^2 = a^2 + 2ab + b^2 es verdadera para todo a y b.

2

La igualdad a^2 - b^2 = (a-b)(a+b) es una identidad algebraica.

3

La expresión a^2 + b^2 = 2ab es verdadera para todo a y b.

4

La igualdad a^2 - b^2 = (a-b)(a+b) se verifica para todos a,b.

5

Si a=0 y b es cualquier número, entonces a^2 + 2ab + b^2 = b^2.

6

La ecuación a^2 + b^2 = 2ab es una identidad algebraica.

7

Si a=b, entonces a^2 - b^2 = 0.

8

La igualdad (a+b)(a-b) = a^2 - b^2 es verdadera.

9

La identidad 4a^2 - 4ab + b^2 = (2a - b)^2 es correcta.

10

Si a = -b, entonces a^2 = b^2.

Explicación

Es una identidad algebraica conocida. Se cumple para todo valor de a y b.

Es la factorización clásica de la diferencia de cuadrados, válida para cualquier a,b.

No es una identidad; solo se cumple si a y b son iguales en ciertos casos, pero no para todos.

Es una identidad válida para cualquier par de números a,b.

Al asignar a=0, la expresión se reduce a b^2, igual a b^2.

No se cumple para todos los pares (a,b); no es una identidad.

Cuando a=b, (a^2 - b^2) se factoriza y se anula.

Es la definición de la diferencia de cuadrados.

Al expandir (2a - b)^2 se obtiene 4a^2 - 4ab + b^2.

El valor cúbico no importa; la magnitud cuadrática es igual.

 
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