Find the volume of the cuboid with dimensions $(x - 1), (x - 2)$ and $(x - 3)$ .

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Solution

We have to find $(x - 1) (x - 2) (x - 3)$ . In the identity
$(x + a) (x + b) (x + c) = x^{3} + x^{2} (a + b + c) + x (a b + b c + c a) + a b c$
We take $a = - 1$ , $b = - 2$ and $c = - 3$ .Hence
$a + b + c = - 6, a b + b c + c a = 2 + 6 + 3 = 11, a b c = - 6$
We obtain the volume as
$x^{3} - 6 x^{2} + 11 x - 6$

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