What is the coefficient of $x^{3}$ in (2x-4) $(x + 6)^{2}$ ?

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Solution

The correct option is A
2

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

(2x-4)( $x + 6)^{2}$ = (2x-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 $x^{3}$ in (2x-4) $(x + 6)^{2}$ is 2

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