Which expression is equivalent to (x2 + 11)2 + (x - 5)(x + 5)?

Explanation

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.