Question

In both Algebraic Identities and Equations L.H.S. = R.H.S., then why do

identities hold true for every value of variables, whereas equations don’t? (Support your

answer with calculations/worked examples if any required).

Equation: 2x - 3 = 5x + 12

Identity: (a + b)*2
= a*2

+ 2 + *2

​

Answer 1

Answer:

Identities are the general expressions for any algebraic operation.

For example, (a-b) ² = a² + b² - 2ab

Here, a and b can be replaced by any number of your choice because the mathematical process is same for every expression.

Like, take a = 2 and b = 3.

Therefore, we will get (2-3)² = 2² + 3² - 2 x 3 x 2

= 1.

Now you could've just subtracted the numbers in bracket and get the answer without applying identity but we cannot just subtract like that with algebraic terms, hence we use identities.

Algebraic equations are not general terms but a particular case for any given expression. But they still hold true for any value of variable in the equation, you just cannot apply the equation to other equation like identity because they are two different things.

Like 2x + 3 = 4.

You can just find the value of this equation, but how would you apply the principle to other equation? It does not make sense.

Equations are unique, Identities are general