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

2 x^{3} - 2 x^{2} - 5 x + 6

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x^{3} - 2 x^{2} - 5 x + 6

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x^{3} - 2 x^{2} - 2 x + 6

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x^{3} - 2 x^{2} - 5 x + 8

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Solution

The correct option is B $x^{3} - 2 x^{2} - 5 x + 6$
Volume of the cuboid $= l e n g t h \times b r e a d t h \times h e i g h t$
$= (x + 2) \times (x - 1) \times (x - 3)$

Using Identity
$(x + a) (x + b) (x + c) = x^{3} + (a + b + c) x^{2} + (a b + b c + c a) x + a b c$

We get,
$(x + 2) \times (x - 1) \times (x - 3) = (x)^{3} + (2 - 1 - 3) (x)^{2} + (2 \times (- 1) + (- 1) \times (- 3) + (- 3) \times 2) x + (2) (- 1) (- 3)$

$= x^{3} - 2 x^{2} + (- 2 + 3 - 6) x + 6$

$= x^{3} - 2 x^{2} - 5 x + 6$

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