# Conjugate

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

It is only used in expressions with **two terms** (called "binomials")

### Other examples:

Expression | Its Conjugate |
---|---|

x^{2} - 3 |
x^{2} + 3 |

a + b | a - b |

a - b^{3} |
a + b^{3} |

## Examples of Use

The conjugate can be very useful because ...

... when we multiply something by its conjugate we get **squares** like this:

### How does that help?

It can help us move a square root from the bottom of a fraction to the top, or vice versa (read Rationalizing the Denominator to find out more):

**Example: **Move the square root of 2 to the top:

Answer: * Multiply both top and bottom by the conjugate* (this will not change the value of the fraction):

(Did you see how the denominator became **a ^{2}-b^{2 }**?)

Get your calculator and work out the value before and after, is it the same?

There is another example on the page Evaluating Limits (advanced topic) where I move a square root from the top to the bottom.

So try to remember this little trick, it may help you solve an equation one day!