(x + 2y)² + (x - 2y)² is equal to:

1. 2x² + 8y² + 8xy

2. x² + 4y²

3. 2x² + 8y²

4. 2x² - 8y²

(x + 2y)² + (x - 2y)²

And using the formula,

[∵(x + y)² = x² + 2xy + y²]

and,

[∵(x - y)² = x² - 2xy + y²]

= [x² + 2 $\times$ x $\times$ 2y + (2y)²] + [x² - 2 $\times$ x $\times$ 2y + (2y)²]

= [x² + 4xy + 4y²] + [x² - 4xy + 4y²]

= x² + 4xy + 4y² + x² - 4xy + 4y²

= (x² + x²) + (4xy - 4xy) + (4y² + 4y²)

= 2x² + 8y²

Hence, option 3 is the correct option.