Simplifying (xy)(xy)
The expression (xy)(xy) can be simplified using the distributive property or by recognizing it as a special product. Let's explore both methods.
Using the Distributive Property
The distributive property states that a(b+c) = ab + ac. We can apply this to our expression by considering (xy) as a single term:

Distribute the first (xy): (xy)(xy) = (xy) * x + (xy) * (y)

Distribute again: = xx  yx + x*(y)  y*(y)

Simplify: = x²  xy  xy + y²

Combine like terms: = x²  2xy + y²
Recognizing the Special Product
The expression (xy)(xy) is a perfect square trinomial. This is because it's the square of a binomial:
(x  y)² = (x  y)(x  y)
The general formula for a perfect square trinomial is:
(a  b)² = a²  2ab + b²
Applying this to our problem, we see that:
 a = x
 b = y
Therefore, we can directly simplify:
(x  y)² = x²  2xy + y²
Conclusion
Both methods lead to the same simplified expression: x²  2xy + y². Using the distributive property demonstrates the process in detail, while recognizing the special product provides a shortcut for solving this type of problem.