Choice D is correct. For the expression $64 t squared s cubed minus 56 t cubed s$ , $4$ is a common factor of $64$ and $56$ , $t^{2}$ is a common factor of $t^{2}$ and $t^{3}$ , and $s$ is a common factor of $s^{3}$ and $s$ . It follows that $4 t squared s$ is a common factor of each term in the given expression. Factoring out $4 t squared s$ from each term in the expression $64 t squared s cubed minus 56 t cubed s$ yields $4 t squared s left parenthesis 16 s squared minus 14 t right parenthesis$ . Therefore, $4 t squared s left parenthesis 16 s squared minus 14 t right parenthesis$ is equivalent to $64 t squared s cubed minus 56 t cubed s$ .

Choice A is incorrect. This expression is equivalent to $64 t s cubed minus 56 t squared s squared$ , not $64 t squared s cubed minus 56 t cubed s$ .

Choice B is incorrect. This expression is equivalent to $64 t cubed s cubed minus 56 t squared s$ , not $64 t squared s cubed minus 56 t cubed s$ .

Choice C is incorrect. This expression is equivalent to $64 t cubed s squared minus 56 t squared s squared$ , not $64 t squared s cubed minus 56 t cubed s$ .

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