What expressions are equivalent to 16x^4 + 64? Please check all that apply.

The expression 16x⁴ + 64 can be factored and expressed in several equivalent forms. Let’s break it down:

• 8(2x⁴ + 8): This is one equivalent expression obtained by factoring out the common factor of 8.
• 16(x⁴ + 4): This shows the expression factored with a combination of 16 and transformation into a simpler polynomial.
• (4x² + 8)(4x² – 8): This represents a factorization using the difference of squares method without the constants.

So, to check all that apply:

• Option 1: 8(2x⁴ + 8)
• Option 2: 16(x⁴ + 4)
• Option 3: (4x² + 8)(4x² – 8)

Each of these alternatives expresses the same quantity in different ways. It’s essential for algebraic simplification and problem-solving to recognize such equivalents.