Which expressions are equivalent to 16x^4 + 64? Check all that apply.

To find expressions that are equivalent to 16x⁴ + 64, we need to factor the expression. The first step is recognizing that both terms have a common factor of 16:

• Factoring out 16 gives us: 16(x⁴ + 4)

Next, we can observe that x⁴ + 4 is a sum of squares, which does not factor nicely in the real numbers, but if we were looking for equivalent expressions, we could also express it using imaginary numbers:

• x⁴ + 4 = (x² + 2i)(x² – 2i)
• Thus, we can write it as 16((x² + 2i)(x² – 2i))

Other simplified forms like 16x⁴ + 64 = 16(x⁴ + 4) or retaining the original form are also equivalent. It is also important to check any expressions provided in your options to see if they simplify to one of the forms we’ve noted.

In conclusion, the expressions equivalent to 16x⁴ + 64 could be expressed as 16(x⁴ + 4) or other variations involving the factor of 16 and the form of x⁴ + 4.