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Advanced Math / Equivalent expressions Difficulty: Medium

Which expression is equivalent to $6 x Superscript 8 Baseline y squared plus 12 x squared y squared$ ?

$6 x squared y squared left parenthesis 2 x Superscript 6 Baseline right parenthesis$

$6 x squared y squared left parenthesis x Superscript 4 Baseline right parenthesis$

$6 x squared y squared left parenthesis x Superscript 6 Baseline plus 2 right parenthesis$

$6 x squared y squared left parenthesis x Superscript 4 Baseline plus 2 right parenthesis$

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Explanation

Choice C is correct. Since each term of the given expression has a common factor of $6 x squared y squared$ , it may be rewritten as $6 x squared y squared left parenthesis x Superscript 6 Baseline right parenthesis plus 6 x squared y squared left parenthesis 2 right parenthesis$ , or $6 x squared y squared left parenthesis x Superscript 6 Baseline plus 2 right parenthesis$ .

Choice A is incorrect. This expression is equivalent to $12 x Superscript 8 Baseline y squared$ , not $6 x Superscript 8 Baseline y squared plus 12 x squared y squared$ .

Choice B is incorrect. This expression is equivalent to $6 x Superscript 6 Baseline y squared$ , not $6 x Superscript 8 Baseline y squared plus 12 x squared y squared$ .

Choice D is incorrect. This expression is equivalent to $6 x Superscript 6 Baseline y squared plus 12 x squared y squared$ , not $6 x Superscript 8 Baseline y squared plus 12 x squared y squared$ .