question_answer

Find the volume of cuboid whose dimensions are \[\left( {{x}^{2}}-2 \right),\left( 2x+2 \right)\text{ }and\text{ }\left( x-1 \right).\]

Answer:

Volume of a cuboid = Length \[\times \] Breadth \[\times \] Height

\[=\left( {{x}^{2}}-2 \right)\left[ \left( 2x+2 \right)\left( x-1 \right) \right]\]

\[=\left( {{x}^{2}}-2 \right)[2{{x}^{2}}-2x+2x-2]~~\]

\[=({{x}^{2}}-2)[2{{x}^{2}}-2]\]

\[=2\left( {{x}^{2}}-2 \right)\left( {{x}^{2}}-1 \right)\]

\[=2\left[ {{x}^{4}}-{{x}^{2}}-2{{x}^{2}}+2 \right]\]

\[=2\left[ {{x}^{4}}-3{{x}^{2}}+2 \right]~~\]

\[=2{{x}^{4}}-6{{x}^{2}}+4\]