Explanation:

x(x + a) (x + 2a) (x + 3a)
= (x² + ax) (x² + 5ax + 6a²)
= x⁴ + ax³ + 5a³ + 5a² x² + 6a² x² + 6a³x
= x⁴ + ax(x² + 5x² + 5ax + 6ax + 6a²)
= x⁴ + ax(6x² + 11ax + 6a²) ... (i)
So, for terms to be perfect square, = (x + y⁾²
(x + y)²= (x² + 2xy + y²) (x² + y²+ 2xy)
= x⁴ + 2x³ y + x² y² + x² y² + 2xy³ + y⁴ + 2x³y + 4x² y² + 2xy³
= x⁴ + xy(4x² + 6xy + 4y²) + y⁴
On comparing equations. (i) and (ii), as y = a
a⁴ must be added to make it a perfect square.