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Which expression is equivalent to +11^2 + x−5 x+5 x^2? +23x^2 −14
Correct answer: B (parsed from the explanation — this source omits an answer key for this item)
Explanation
2+11 2 Choice B is correct. The expression ^x h can be written as 2+11 2+11 2 2+11+11 2+11 2 ^x h^x h, which is equivalent to x ^x h ^x h. Distributing x 2+11 4+11 2+11 2+121 4+22 2+121 and 11 to ^x h yields x x x , or x x . The - + - + - expression ^x 5h^x 5h is equivalent to ^x 5hx ^x 5h5. Distributing x and 5 - 2-5 +5 -25 2-25 to ^x 5h yields x x x , or x . Therefore, the expression 2+11 2+ -5 +5 4+22 2+121+ 2-25 ^x h ^x h^x h is equivalent to ^x x h ^x h, or 4+22 2+121+ 2-25 x x x . Combining like terms in this expression yields 4+23 2+96 x x . Choice A is incorrect. Equivalent expressions must be equivalent for any value of -14 x. Substituting 0 for x in this expression yields , whereas substituting 0 for 96 x in the given expression yields . Choice C is incorrect. Equivalent expressions must be equivalent for any value of x. Substituting 0 for x in this expression 121 96 yields , whereas substituting 0 for x in the given expression yields . Choice D is incorrect. Equivalent expressions must be equivalent for any value of 146 x. Substituting 0 for x in this expression yields , whereas substituting 0 for x 96 in the given expression yields .
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