The product of
$(6 a^{2} - 7 b + 5 a b) and 2 a b$ is _____.

12 a^{3} b - 10 a^{2} b^{2} + 14 a b^{2}

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12 a^{3} b + 10 a^{2} b^{2} - 14 a b^{2}

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6 a^{3} b + 5 a^{2} b^{2} - 7 a b^{2}

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12 a^{2} b + 10 a^{3} b^{2} - 14 a b^{2}

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Solution

The correct option is B $12 a^{3} b + 10 a^{2} b^{2} - 14 a b^{2}$
$= (6 a^{2} - 7 b + 5 a b) \times 2 a b$
$= (2 a b \times 6 a^{2}) - (7 b \times 2 a b) + (5 a b \times 2 a b)$
$= 12 a^{3} b - 14 a b^{2} + 10 a^{2} b^{2}$
$= 12 a^{3} b + 10 a^{2} b^{2} - 14 a b^{2}$

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