Answer:
( y + b - a - 3d)(y + b + a + 3d).
Step-by-step explanation:
y^2 + 2by + b^2 - a^2 - 6ad - 9d^2
= y^2 + 2by + b^2 - (a^2 + 6ad + 9d^2)
= (y + b)^2 - (a + 3d)^2
This is the difference of 2 squares so we have
(y + b - (a + 3d))(y + b + (a + 3d))
= ( y + b - a - 3d)(y + b + a + 3d)
