Mathematical identities | Algebra | Elementary algebra

Brahmagupta's identity

In algebra, Brahmagupta's identity says that, for given , the product of two numbers of the form is itself a number of that form. In other words, the set of such numbers is closed under multiplication. Specifically: Both (1) and (2) can be verified by expanding each side of the equation. Also, (2) can be obtained from (1), or (1) from (2), by changing b to −b. This identity holds in both the ring of integers and the ring of rational numbers, and more generally in any commutative ring. (Wikipedia).

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Related pages

Brahmagupta matrix | Chakravala method | Arithmetica | Fibonacci | Pell's equation | Polynomial expansion | Rational number | Brahmagupta's interpolation formula | Closure (mathematics) | Diophantus | Integer | The Book of Squares | Brahmagupta–Fibonacci identity | Algebra | Commutative ring