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Advanced Math / Equivalent expressions Difficulty: Medium

Which expression is equivalent to $(d - 6) (8 d^{2} - 3)$ ?

$8 d^{3} - 14 d^{2} - 3 d + 18$

$8 d^{3} - 17 d^{2} + 48$

$8 d^{3} - 48 d^{2} - 3 d + 18$

$8 d^{3} - 51 d^{2} + 48$

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Explanation

Choice C is correct. Applying the distributive property to the given expression yields $d (8 d^{2} - 3) - 6 (8 d^{2} - 3)$ . Applying the distributive property once again to this expression yields $(d) (8 d^{2}) + (d) (- 3) + (- 6) (8 d^{2}) + (- 6) (- 3)$ , or $8 d^{3} + (- 3 d) + (- 48 d^{2}) + 18$ . This expression can be rewritten as $8 d^{3} - 48 d^{2} - 3 d + 18$ . Thus, $(d - 6) (8 d^{2} - 3)$ is equivalent to $8 d^{3} - 48 d^{2} - 3 d + 18$ .

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.