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Advanced Math / Equivalent expressions Difficulty: Easy

$open parenthesis, 2 x cubed, plus 3 x, close parenthesis, times, open parenthesis, x cubed, minus 2 x, close parenthesis$

Which of the following is equivalent to the expression above?

$x cubed, plus 5 x$

$3 x cubed, plus x$

$2 x to the sixth power, minus x to the fourth power, minus 6 x squared$

$3 x to the sixth power, minus x to the fourth power, minus 6 x squared$

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Explanation

Choice C is correct. Using the distributive property to multiply the terms in the parentheses yields $open parenthesis, 2 x cubed, times x cubed, close parenthesis, plus, open parenthesis, 2 x cubed, times negative 2 x, close parenthesis, plus, open parenthesis, 3 x times x cubed, close parenthesis, plus, open parenthesis, 3 x times negative 2 x, close parenthesis$ , which is equivalent to $2 x to the sixth power minus 4 x to the fourth power, plus 3 x to the fourth power, minus 6 x squared$ . Combining like terms results in $2 x to the sixth power minus x to the fourth power, minus 6 x squared$ .

Choices A and D are incorrect and may result from conceptual errors when multiplying the terms in the given expression. Choice B is incorrect and may result from adding, instead of multiplying, $open parenthesis, 2 x cubed, plus 3 x, close parenthesis$ and $open parenthesis, x cubed, minus 2 x, close parenthesis$ .