Determine the values for "a" and "b." The basic form that a conjugate takes is (a - b) or (a + b). When looking at a binomial, you will need to determine what the value is for "a" and what the value is for "b." After you figure out this information, creating the conjugate is rather simple. For instance, if the binomial is 3x - 2y, you would determine that "a" is 3x and "b" is -2y.
Negate one of the terms. Either negate the "a" term or the "b" term, but not both. For instance, if "a" is 3x and "b" is -2y, you could negate the "b" term. This would mean "b" is - (-2y) or "b" is 2y. You could alternatively negate the "a" term to get a different conjugate; either is correct.
Create the final conjugate. Combine the two terms, "a" and "b," to create the final conjugate. With the running example, "a" is 3x and "b" is 2y, so the conjugate would be 3x + 2y.
Check your work. The conjugate multiplied by the original binomial should result in a^2 - b^2 if the numbers are real. Alternatively, if the numbers are complex and there is a term for "i" indicating an imaginary number, the result would be a^2 + b^2. Using the running example, the original binomial multiplied by the conjugate gives (3x - 2y) x (3x + 2y) = 9x^2 - 4y^2, which is in the form a^2 - b^2.