What is the coefficient of $x^{2}$ in $(2 x - 4) (x + 6)^{2}$ ?

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Solution

The correct option is A
20

We use the identity $(a + b)^{2} = a^{2} + b^{2} + 2 a b$ to expand the second term.

$(2 x - 4) (x + 6)^{2} = (2 x - 4) (x^{2} + 36 + 12 x)$

$= 2 x^{3} + 72 x + 24 x^{2} - 4 x^{2} + 32 - 48 x$

$= 2 x^{3} + 72 x + 20 x^{2} + 32 - 48 x$

The coefficient of $x^{2}$ in $(2 x - 4) (x + 6)^{2}$ is 20

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