Which expression is equivalent to x 2 + 11 2 + x - 5 x + 5 ?

Question

Accepted Answer

Choice B is correct. The expression x 2 + 11 2 can be written as x 2 + 11 x 2 + 11 , which is equivalent to x 2 x 2 + 11 + 11 x 2 + 11 . Distributing x 2 and 11 to x 2 + 11 yields x 4 + 11 x 2 + 11 x 2 + 121 , or x 4 + 22 x 2 + 121 . The expression x - 5 x + 5 is equivalent to x - 5 x + x - 5 5 . Distributing x and 5 to x - 5 yields x 2 - 5 x + 5 x - 25 , or x 2 - 25 . Therefore, the expression x 2 + 11 2 + x - 5 x + 5 is equivalent to x 4 + 22 x 2 + 121 + x 2 - 25 , or x 4 + 22 x 2 + 121 + x 2 - 25 . Combining like terms in this expression yields x 4 + 23 x 2 + 96 . Choice A is incorrect. Equivalent expressions must be equivalent for any value of x . Substituting 0 for x in this expression yields - 14 , whereas substituting 0 for x in the given expression yields 96 . Choice C is incorrect. Equivalent expressions must be equivalent for any value of x . Substituting 0 for x in this expression yields 121 , whereas substituting 0 for x in the given expression yields 96 . Choice D is incorrect. Equivalent expressions must be equivalent for any value of x . Substituting 0 for x in this expression yields 146 , whereas substituting 0 for x in the given expression yields 96 .

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