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Equivalent expressions SAT question

Math · Advanced Math · Easy · Answer it here, explanation included.

Which expression is equivalent to $256 w^{2} - 676$ ?

ExplanationShow

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 $256 w^{2} - 676$ can be written as $(16 w)^{2} - 26^{2}$ , or $(16 w) (16 w) - (26) (26)$ , 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 $64 w^{2} - 169$ .

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

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Equivalent expressions SAT question

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