What is a conjugate and what is it used for

Conjugate

The conjugate is where we change the sign in the middle of two terms like this:

conjugate of 3x+1 is 3x-1

We only use it in expressions with two terms, called "binomials":

Binomial

Here are some more examples:

Expression Its Conjugate

x2 - 3 ⇒ x2 + 3

a + b ⇒ a - b

a - b3 ⇒ a + b3