What is the missing term in the following product?
$({2 a}^{3} - 3) ({5 a}^{3} - 2) = {10 a}^{6} + . . . . . + 6$

{19 a}^{3}

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{- 19 a}^{3}

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{16 a}^{3}

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{- 16 a}^{3}

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Solution

The correct option is D ${- 19 a}^{3}$

We need to find missing term in $(2 a^{3} - 3) (5 a^{3} - 2) = 10 a^{6} + . . . . . + 6$
$({2 a}^{3} - 3) ({5 a}^{3} - 2)$
$= {2 a}^{3} ({5 a}^{3} - 2) - 3 ({5 a}^{3} - 2)$
$= {10 a}^{6} - {4 a}^{3} - {15 a}^{3} + 6$
$= {10 a}^{6} - {19 a}^{3} + 6$
Hence, missing term is $- 19 a^{3}$ .

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