If a + b + c = 4,
ab + bc + ca = 6
and abc = 3,

what are the values of:
1/a + 1/b + 1/c,
(think of fractions),
1/ab + 1/bc + 1/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.