If $a+b+c=4$,
$ab+bc+ca=6$
and $abc=3$,
what are the values of:
$${1\over a}+ {1\over b }+ {1\over c}$$
(think of fractions),
$${1\over ab}+ {1\over bc }+ {1\over ca}$$
and
$$a^2 +b^2 + c^2$$?
In the diagram the coloured squares have sides
of length a, b and c. Use the areas in the
diagram to write down a formula for the
expansion of (a + b + c)2 and explain your
method.
Now think of a cube where each face is cut up
in a similar way and use it to write down a
formula for the expansion of (a + b + c)3
