question_answer

The length and breadth of a rectangle are \[3{{x}^{2}}-2\text{ }and\text{ }2x+5\]respectively. Find its area.

Answer:

Here,                      length \[3{{x}^{2}}-2\]

breadth = 2x + 5

Area = (length) \[\times \] (breadth)

\[=(3{{x}^{2}}-2)\times 2(2x+5)\]

\[=3{{x}^{2}}(2x+5)+(-2)(2x+5)\]

\[=6{{x}^{3}}+15{{x}^{2}}-4x-10\]

Thus, the required area of the rectangle is

\[6{{x}^{3}}-15{{x}^{2}}-4x-10\] sq. units.