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Theorem

Difference of Two Squares

Algebra

The difference of two squares is an algebraic identity describing what happens when one squared quantity is subtracted from another. It states that for any two numbers or expressions a and b, a squared minus b squared always factors as the product of their sum and their difference, that is, as the quantity a plus b times the quantity a minus b. The two quantities a and b need not be simple numbers; they can themselves be more complicated expressions, and the identity still lets their squared difference be factored the same way. Run in the opposite direction, the identity also shows that the product of any two numbers can be written as the square of their average minus the square of half their difference, a fact used in a variety of algebraic manipulations and mental arithmetic shortcuts.

Facts
Classification
Statement Form
Identity or Equation 1
Statement
a^2 - b^2 = (a + b)(a - b). 1
Connections

Has Statement Form

Equation, Concepts

Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.

Identity, Concepts

Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.

In Branch

Source Difference of two squares (Wikipedia)
Sources
1. Difference of two squares (Wikipedia)
  • Introduction
    a² − b² = (a + b)(a − b).
  • In Branch: Algebra, Lead sentence
    In elementary algebra, a difference of two squares is one squared number (the number multiplied by itself) subtracted from another
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