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Advanced Math / Equivalent expressions Difficulty: Easy

Which expression is equivalent to $13 x squared minus 7 x squared$ ?

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Explanation

Choice B is correct. Since each term in the given expression has a common factor of $x^{2}$ , it can be rewritten as $left parenthesis 13 minus 7 right parenthesis x squared$ , or $6 x squared$ . Therefore, the expression $6 x squared$ is equivalent to $13 x squared minus 7 x squared$ .

Alternate approach: Since the two terms of the given expression are both constant multiples of $x^{2}$ , they are like terms and can, therefore, be combined through subtraction. Subtracting like terms in the expression $13 x squared minus 7 x squared$ yields $6 x squared$ .

Choice A is incorrect. This expression is equivalent to $left parenthesis 13 x right parenthesis left parenthesis minus 7 x right parenthesis$ , not $13 x squared minus 7 x squared$ .

Choice C is incorrect. This expression is equivalent to $13 x squared plus 7 x squared$ , not $13 x squared minus 7 x squared$ .

Choice D is incorrect and may result from conceptual or calculation errors.