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Equivalent expressions SAT question

Math · Advanced Math · Easy · Answer it here, explanation included.

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 ?

ExplanationShow

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.

 

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