Correct Option: A

(x – 1) (x + 5) (x + 1) (x + 3) + 7
= (x² + 5x – x – 5) (x² + 3x + x + 3) + 7
= (x² + 4x – 5) (x² + 3x + x + 3) + 7
Putting x² + 4x = y, we have,
Expression = (y – 5) (y + 3) + 7
= y² – 5y + 3y – 15 + 7
= y² – 2y – 8
= y² – 4y + 2y – 8
= y (y – 4) + 2 (y – 4)
= (y + 2) (y – 4)
Now,
y + 2 = x² + 4x + 2
= x² + 4x + 2 – 2
= (x + 2)² – (√2)²
(x + 2 + √2)(x + 2 − √2)
Again, y – 4
= x² + 4x – 4
= x² + 4x + 4 – 8
= (x + 2)² – (2√2)²
= (x + 2 + 2√2)(x + 2 − 2√2)
∴  Factorisation is
= (x + 2 + √2)(x + 2 − √2)
(x + 2 + 2√2)(x + 2 − 2√2)