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Advanced Math / Equivalent expressions Difficulty: Medium

$open parenthesis, 4, x cubed, minus 5, x squared, plus 3, close parenthesis, minus, open parenthesis, 6, x cubed, plus 2, x squared, minus x, close parenthesis$

Which of the following expressions is equivalent to the expression above?

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Explanation

Choice B is correct. Using the distributive property, the given expression can be rewritten as $4 x cubed, minus 5 x squared, plus 3, minus 6 x cubed, minus 2 x squared, plus x$ . Combining like terms, this expression can be rewritten as $open parenthesis, 4 minus 6, close parenthesis, times x cubed, plus, open parenthesis, negative 5 minus 2, close parenthesis, times x squared, plus x, plus 3$ , which is equivalent to $negative 2 x cubed, minus 7 x squared, plus x, plus 3$ .

Choices A, C, and D are incorrect and may result from an error when applying the distributive property or an error when combining like terms.