To simplify the given expression, we can use the trigonometric identity:

sin^2(a) + cos^2(a) = 1

First, let's rewrite the expression in terms of sin^2(a) and cos^2(a):

sin^4(a) + 2sin^2(a)cos^2(a) + cos^4(a) = (sin^2(a))^2 + 2(sin^2(a))(cos^2(a)) + (cos^2(a))^2

Then we can factor out sin^2(a) and cos^2(a):

(sin^2(a) + cos^2(a))^2 = 1^2

= 1

Therefore, the given expression simplifies to:

sin^4(a) + 2sin^2(a)cos^2(a) + cos^4(a) = 1

So, the equation sin^4(a) + 2sin^2(a)cos^2(a) + cos^4(a) = 0 is not correct.