Which expression is equivalent to (x² + 4)² + (x-2) (x+2) ? (May 2023 U.S.)

Correct answer: D) x⁴ + 9x² + 12.
Given: (x² + 4)² + (x-2) (x+2)

Step 1: Expand the first term using the formula (a+b)² = a² + 2ab + b²:
(x² + 4)² = (x²)² + 2(x²)(4) + 4² = x⁴ + 8x² + 16

Step 2: Expand the second term using the difference of squares formula (a-b)(a+b) = a² - b²:
(x-2)(x+2) = x² - 2² = x² - 4

Step 3: Combine the results from steps 1 and 2:
x⁴ + 8x² + 16 + (x² - 4)

Step 4: Simplify by combining like terms:
x⁴ + 8x² + 16 + x² - 4 = x⁴ + 9x² + 12

Therefore, the equivalent expression is:
D) x⁴ + 9x² + 12