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Advanced Math / Equivalent expressions Difficulty: Easy

Which expression is equivalent to $17 left parenthesis x squared minus 100 y squared right parenthesis$ ?

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Explanation

Choice D is correct. Expressions in the form $a^{2} - b^{2}$ follow the difference of two squares pattern and can be factored as $(a - b) (a + b)$ . In the given expression, $17 left parenthesis x squared minus 100 y squared right parenthesis$ , the expression $x squared minus 100 y squared$ follows the difference of two squares pattern. It follows that the expression $x squared minus 100 y squared$ can be rewritten as $(x - 10 y) (x + 10 y)$ . Therefore, the expression $17 (x - 10 y) (x + 10 y)$ is equivalent to $17 left parenthesis x squared minus 100 y squared right parenthesis$ .

Choice A is incorrect. This expression is equivalent to $17 (x^{2} - 52 x y + 100 y^{2})$ , not $17 left parenthesis x squared minus 100 y squared right parenthesis$ .

Choice B is incorrect. This expression is equivalent to $17 (x^{2} + 48 x y - 100 y^{2})$ , not $17 left parenthesis x squared minus 100 y squared right parenthesis$ .

Choice C is incorrect. This expression is equivalent to $17 (x^{2} - 20 x y + 100 y^{2})$ , not $17 left parenthesis x squared minus 100 y squared right parenthesis$ .