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Advanced Math / Equivalent expressions Difficulty: Easy

Which expression is equivalent to $256 w squared minus 676$ ?

$(16 w - 26) (16 w - 26)$

$(8 w - 13) (8 w + 13)$

$(8 w - 13) (8 w - 13)$

$(16 w - 26) (16 w + 26)$

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Explanation

Choice D is correct. The given expression follows the difference of two squares pattern, $x^{2} - y^{2}$ , which factors as $(x - y) (x + y)$ . Therefore, the expression $256 w squared minus 676$ can be written as $left parenthesis 16 w right parenthesis squared minus 26 squared$ , or $left parenthesis 16 w right parenthesis left parenthesis 16 w right parenthesis minus left parenthesis 26 right parenthesis left parenthesis 26 right parenthesis$ , which factors as $(16 w - 26) (16 w + 26)$ .

Choice A is incorrect. This expression is equivalent to $256 w^{2} - 832 w + 676$ .

Choice B is incorrect. This expression is equivalent to $64 w squared minus 169$ .

Choice C is incorrect. This expression is equivalent to $64 w^{2} - 208 w + 169$ .