Final answer:
The simplified form of sin⁴a cos⁴a - 2sin²a cos²a is sin²a cos²a(sin²a cos²a - 2) after factoring and using trigonometric identities.
Step-by-step explanation:
The simplified form of sin⁴a cos⁴a - 2sin²a cos²a can be found using algebraic identities and trigonometric identities. First, we recognize that the expression resembles the form of a difference of squares, since sin²a cos²a is common in both terms.
Let's let x = sin²a cos²a. Our expression then becomes x² - 2x. Factoring x out, we get x(x - 2). Substituting back in for x, we have sin²a cos²a(sin²a cos²a - 2).
We can also utilize trigonometric identities, particularly the identity sin²a + cos²a = 1, to further simplify the expression if needed to obtain sin⁴a cos⁴a - 2sin²a cos²a = sin²a cos²a(sin²a cos²a - 2).