The length of the rectangle is (4ab + 6) m and breadth of the rectangle is $(6 b^{2} + 2 a b)$ m. Find the area of the rectangle.

(24 a b^{3} + 18 a^{2} b^{2} + 36 b^{2} + 12 a b) m^{2}

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(24 a b^{3} + 6 a^{2} b^{2} + 6 b^{2} + 12 a b) m^{2}

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(24 a b^{3} + 8 a^{2} b^{2} + 36 b^{2} + 12 a b) m^{2}

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(8 a^{2} b^{2} + 36 b^{2} + a b) m^{2}

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Solution

The correct option is C $(24 a b^{3} + 8 a^{2} b^{2} + 36 b^{2} + 12 a b) m^{2}$
Given:
Length of the rectangle = (4ab + 6) m
Breadth of the rectangle = $(6 b^{2} + 2 a b)$ m

Area of a rectangle = length $\times$ breadth
$= (4 a b + 6) \times (6 b^{2} + 2 a b)$
$= 4 a b (6 b^{2} + 2 a b) + 6 (6 b^{2} + 2 a b)$
$= 24 a b^{3} + 8 a^{2} b^{2} + 36 b^{2} + 12 a b$
Hence, area of the rectangle $= (24 a b^{3} + 8 a^{2} b^{2} + 36 b^{2} + 12 a b) m^{2}$ .

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