where
n is any positive whole number.
A Level Maths Notes: C2 – Binomial Expansion
We can use the binomial theorem to expand and simplify expressions
of the form
where
n is any positive whole number.
The general expansions is
Example:
We evaluate the coefficient of each power of
and
simplify:
Example:
which simplifies to
then
Suppose we have an expansion. We know
and
but
not n. If we have a relationship between the coefficients we may be
able to form an equation to find n. Suppose in the expansion below we
know that the coefficient of
equals
the coefficient of
The coefficient of
is
The coefficient of
is
Equate these:
Now
cancel where possible
