4a2 + b2 + 4ab + 8a + 4b + 4 = ?
We have,
4a2 + b2 + 4ab + 8a + 4b + 4
We know that,
x2 + y2 + z2 + 2xy + 2yz + 2xz = (x + y + z)2
= (2a)2 + (b)2 + (2)2 + 2 (2a) (b) + 2 (b) (2) + 2 × 2 (2a)
= (2a + b + 2)2
Hence, option A is correct