Identity and identical expressions

In this publication, we will consider what identity and identical expressions are, list the types, and also give examples for a better understanding.

Definitions of Identity and Identity Expression

Identity is an arithmetic equality whose parts are identically equal.

Two mathematical expressions identically equal (in other words, are identical) if they have the same value.

Identity types:

1. Numeric Both sides of the equation consist only of numbers. For example:
   • 6 + 11 = 9 + 8
   • 25 ⋅ (2 + 4) = 150
2. Literal – identity, which also consists of letters (variables); is true for whatever values ​​they take. For example:
   • 12x + 17 = 15x – 3x + 16 + 1
   • 5 ⋅ (6x + 8) = 30x + 40

Example of a problem

Determine which of the following equalities are identities:

• 212 + x = 2x – x + 199 + 13
• 16 ⋅ (x + 4) = 16x + 60
• 10 – (-x) + 22 = 10x + 22
• 1 – (x – 7) = -x – 6
• x² + 2x = 2x³
• (15 – 3)² = 15² + 2 ⋅ 15 ⋅ 3 – 3²

Answer:

Identities are the first and fourth equalities, because for any values x both parts of them will always take the same values.