OG详解-OG6 数学1 Q12

Choice B is correct. The expression (x² +11)²  can be written as (x² +11)(x² +11), which is equivalent to x² (x² +11)+11(x² +11) . Distributing x² and 11 to (x² +11) yields x⁴ +11x² +11x² +121, or x⁴ +22x² + 121. The expression (x-5)(x+5) is equivalent to (x-5)x+(x-5)5 . Distributing x and 5 to (x-5) yields x² -5x+5x-25, or x² -25. Therefore, the expression (x² +11)² +(x-5)(x+5) is equivalent to (x⁴ +22x² +121)+(x² -25) , or x⁴ +22x² + 121 +x² -25. Combining like terms in this expression yields x⁴ +23x² +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.