Identity vs Equation Math Example 2

Follow the full solution, then compare it with the other examples linked below.

Example 2

medium
Classify: (a) x2−1=(x+1)(x−1)x^2 - 1 = (x+1)(x-1) and (b) x2−1=0x^2 - 1 = 0.

Solution

  1. 1
    (a) Expand (x+1)(x−1)=x2−1(x+1)(x-1) = x^2 - 1. Both sides are always equal, so this is an identity.
  2. 2
    (b) x2−1=0x^2 - 1 = 0 is only true when x=1x = 1 or x=−1x = -1. This is an equation with specific solutions.
  3. 3
    Key difference: (a) is true for all xx; (b) is true for only two values.

Answer

(a) identity, (b) equation
An identity uses the variable as a generalization (true for all values). An equation uses the variable as a placeholder (true for specific values only).

About Identity vs Equation

An identity is an equation that holds true for all possible values of the variable, such as (a+b)2=a2+2ab+b2(a+b)^2 = a^2 + 2ab + b^2. A conditional equation is true only for specific values, like x+3=7x + 3 = 7 (true only when x=4x = 4).

Learn more about Identity vs Equation →

More Identity vs Equation Examples

Example 1 easy

Is [formula] an identity or an equation with specific solutions?

Example 3 easy

Is [formula] an identity or an equation?

Example 4 medium

Is [formula] an identity?

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