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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.
Using your expansion of $(a + b + c)^2$ to help you, expand $(a + b
+ c)^3$. Can you explain each term of the expansion using a diagram
of a cube where each face has been cut up in a similar way to the
square above?