Identity vs Equation Math Example 4

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

Example 4

medium
Is a(b+c)=ab+aca(b + c) = ab + ac an identity?

Solution

  1. 1
    This is the distributive property—it holds for all real numbers aa, bb, cc.
  2. 2
    Yes, it is an identity.

Answer

Yes, it is an identity.
The distributive property is a fundamental algebraic identity. It works for all real numbers, not just specific values.

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 2 medium

Classify: (a) [formula] and (b) [formula].

Example 3 easy

Is [formula] an identity or an equation?

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