Advanced Factoristation
Some expression require a certain amount of recogintion before they can be factorised.
The expression
can be factorised, but only when it is recognised that the first two terms can be factorised as a difference of squares:
The last two terms can also be factorised as
so that
is a common factor.
Some expressions with four terms, involving four different variables, can also be factorised.
The simplest is
Notice that
is a common factor of the first two terms, and
is a common factor of the last two terms. We have
Now
is a common factor, so we can write
Hence