In the expansion of $(2 x^{2} - 8) (x - 4)^{2}$ , find the value of coefficient of $x^{3}$ .

- 16

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- 45

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19

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Solution

The correct option is A $- 16$
$(2 x^{2} - 8) {(x - 4)}^{2}$

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

$= (2 x^{2} - 8) (x^{2} - 8 x + 16)$

$= 2 x^{4} - 16 x^{3} + 32 x^{2} - 8 x^{2} + 64 x - 128$

$= 2 x^{4} - 16 x^{3} + 24 x^{2} + 64 x - 128$

Coefficient of $x^{3}$ is $- 16$

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