## Understanding (x-y)(x-y)

The expression **(x-y)(x-y)** is a common algebraic expression that can be simplified using the **FOIL method** or the **distributive property**.

### Using the FOIL Method

FOIL stands for **First, Outer, Inner, Last**, and it's a systematic way to multiply two binomials.

**First:**Multiply the first terms of each binomial:**x * x = x²****Outer:**Multiply the outer terms of the binomials:**x * -y = -xy****Inner:**Multiply the inner terms of the binomials:**-y * x = -xy****Last:**Multiply the last terms of each binomial:**-y * -y = y²**

Now, combine the terms: **x² - xy - xy + y²**

Finally, simplify by combining like terms: **x² - 2xy + y²**

### Using the Distributive Property

The distributive property states that a(b+c) = ab + ac.

**Distribute the first term:**x(x-y) =**x² - xy****Distribute the second term:**-y(x-y) =**-xy + y²**

Now, combine the terms: **x² - xy - xy + y²**

Finally, simplify by combining like terms: **x² - 2xy + y²**

### Conclusion

Both methods lead to the same simplified answer: **x² - 2xy + y²**. This expression is a **perfect square trinomial**, which is a special case of a trinomial that results from squaring a binomial.

Understanding how to multiply binomials is essential for various algebraic operations, including solving equations, factoring expressions, and simplifying expressions.