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$(2 a + 5) (4 a^{2} - 2 a + 8) = ?$

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$8 a^{3} + 15 a^{2} + 5 a + 45$

$8 a^{3} - 16 a^{2} - 6 a + 40$

$8 a^{3} + 16 a^{2} - 6 a + 30$

$8 a^{3} + 16 a^{2} + 6 a + 40$

answer is D.

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Detailed Solution

$(2 a + 5) (4 a^{2} - 2 a + 8)$

$= 2 a (4 a^{2} - 2 a + 8) + 5 (4 a^{2} - 2 a + 8)$

$= 8 a^{3} - 4 a^{2} + 16 a + 20 a^{2} - 10 a + 40$

Collecting the like terms together, we get

$= 8 a^{3} + (- 4 a^{2} + 20 a^{2}) + (16 a - 10 a) + 40$

$= 8 a^{3} + 16 a^{2} + 6 a + 40$

Hence, $(2 a + 5) (4 a^{2} - 2 a + 8) = 8 a^{3} + 16 a^{2} + 6 a + 40$

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