Difference of two squares
Whenever we have an expression in the form of:
We can factorise it into:
Similarly, if we have an expression in the form of:
We can expand it into:
This has a lot of uses. For example, it’s a key step in the method of rationalising the denominator of a fraction.
Examples
Section titled “Examples”Example: Factorise
Section titled “Example: Factorise ”- We know that
factorises to . - Here,
and (since ). - So,
factorises to .
Answer:
Example: Expand
Section titled “Example: Expand ”- We know that
expands to . - Here,
and . - So,
expands to .
Answer:
Example: Factorise
Section titled “Example: Factorise ”- We know that
factorises to . - Here,
(since ) and (since ). - So,
factorises to .
Answer: