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Advanced Math / Equivalent expressions Difficulty: Easy

Which of the following expressions is equivalent to the sum of $open parenthesis, r cubed, plus 5 r squared, plus 7, close parenthesis$ and $open parenthesis, r squared, plus 8 r, plus 12, close parenthesis$ ?

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Explanation

Choice D is correct. Grouping like terms, the given expressions can be rewritten as $r cubed plus, open parenthesis, 5, r squared plus r squared, close parenthesis, plus 8 r, plus, open parenthesis, 7 plus 12, close parenthesis$ . This can be rewritten as $r cubed, plus 6, r squared, plus 8 r, plus 19$ .

Choice A is incorrect and may result from adding the two sets of unlike terms, $r cubed$ and $r squared$ as well as $5, r squared$ and $8 r$ , and then adding the respective exponents. Choice B is incorrect and may result from adding the unlike terms $r cubed$ and $r squared$ as if they were $r cubed$ and $r cubed$ and adding the unlike terms $5, r squared$ and $8 r$ as if they were $5, r squared$ and $8, r squared$ . Choice C is incorrect and may result from errors when combining like terms.