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

24

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20

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22

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16

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Solution

The correct option is A $24$
$(2 x^{2} - 8) {(x - 4)}^{2}$
$= (2 x^{2} - 8) (x^{2} - 2 x (4) + 4^{2})$
$= (2 x^{2} - 8) (x^{2} - 8 x + 16)$
$= 2 x^{4} - 16 x^{3} + 32 x^{2} - 8 x^{2} + 64 x - 128$
$= 2 x^{4} - 16 x^{3} + 24 x^{2} + 64 x - 128$
Coefficient of $x^{2}$ is $24$

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