1. Conjugates Surds By
Mr Porter

2. What is a CONJUGATE?
Given an expression such as (x + y), then its conjugate is (x – y).
The two expression only differ by the operator, that ‘+’ and ‘–’ .
Expression
Conjugate
a – b
a + b
To write a conjugate, simply re-write the expression and change the ‘+’ to a ‘–’ or “–’ to a ‘+’.
a – 5
a + 5
x + 1
x – 1
x + y
x – y
3x + √2
3x – √2

3. Why are conjugates so interesting?
Answer is in the binomial expansion.
Notice the SURD term disappears!
Notice the SURD term disappears!
Notice the SURD term disappears!

4. Notice, it is always the SUBTRACTION of ( )2 – ( )2.
What is important!
So, this gives us a SHORT cut to the answer, if we multiply a pair of CONJUGATE EXPRESSIONS.
Example: Expand (and simplify) 1) 2) 3)
Notice, it is always the SUBTRACTION of ( )2 – ( )2.

5. Notice, it is always the SUBTRACTION of ( )2 – ( )2.
Product of CONJUGATES:
Examples: 1) 2) 3) 4) 5) 6)
Notice, it is always the SUBTRACTION of ( )2 – ( )2.