# Conjugate (algebra)

In algebra, a conjugate is a binomial formed by negating the second term of a binomial. The conjugate of x + y is xy, where x and y are real numbers. If y is imaginary, the process is termed complex conjugation: the complex conjugate of a + bi is abi, where a and b are real.

## Differences of squares

In a commutative ring, an expression of the form

${\displaystyle a^{2}-b^{2}}$

can be factored to give

${\displaystyle (a+b)(a-b)}$

where one factor is the conjugate of the other. This can be useful when trying to rationalize a denominator containing radicals.