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Advanced Math / Equivalent expressions Difficulty: Medium

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

$8 x cubed plus 6$

$7 x cubed plus 10$

$8 x cubed plus 10$

$7 x cubed plus 6$

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Explanation

Choice B is correct. The given expression is equivalent to $8 x^{3} + 8 - x^{3} - (- 2)$ , or $8 x^{3} + 8 - x^{3} + 2$ . Combining like terms in this expression yields $7 x cubed plus 10$ .

Choice A is incorrect. This expression is equivalent to $(8 x^{3} + 8) - 2$ , not $(8 x^{3} + 8) - (x^{3} - 2)$ .

Choice C is incorrect. This expression is equivalent to $(8 x^{3} + 8) - (- 2)$ , not $(8 x^{3} + 8) - (x^{3} - 2)$ .

Choice D is incorrect. This expression is equivalent to $(8 x^{3} + 8) - (x^{3} + 2)$ , not $(8 x^{3} + 8) - (x^{3} - 2)$ .