The binomial Theorem allows us to expand many brackets
without multiplying each bracket out one by one. It states:
To expand
we
could expand
which
would be a very long winded process. Or we could just substitute
for
and
into
the expression for the binomial expansion. Example: Expand
then
we
could expandwhich
would be a very long winded process. Or we could just substitute
forandinto
the expression for the binomial expansion. Example: Expandthen
which simplifies to
and further to
We may be asked to solve questions involving the coefficients. For example, the coefficient of
in
the binomial expansion of
is
equal to 3 times the coefficient of
.Find n.Using the binomial expansion, the coefficient of
is
Using the binomial expansion, the coefficient of
is
Hence we can write down the equation
Now we have to perform some trickery:
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