Conjugates
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Conjugates
The factors of a difference of squares, where \(a^2 - b^2 = \left( {a + b} \right)\left( {a - b} \right)\), are known as conjugates. A conjugate is a binomial with the same two terms as the first binomial, but with the opposite sign in front of the second term.
As seen in the Investigation, when a binomial with at least one square root is multiplied by its conjugate, the result is an expression with no radicals. When given a rational expression containing radicals in the binomial denominator, you can use the conjugate of the denominator to rationalize the denominator.
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Conjugates
The binomials \((a + b)\) and \((a - b)\) are conjugates, and their product is \(a^2 - b^2\).