## Expanding (x - 5y)2

The expression (x - 5y)2 represents the square of a binomial, which is a polynomial with two terms. To expand this, we can apply the **FOIL** method (First, Outer, Inner, Last) or the **Square of a Binomial** formula.

### Using the FOIL Method

**First:**Multiply the first terms of each binomial: x * x =**x²****Outer:**Multiply the outer terms: x * (-5y) =**-5xy****Inner:**Multiply the inner terms: (-5y) * x =**-5xy****Last:**Multiply the last terms: (-5y) * (-5y) =**25y²**

Now, add all the terms together:
x² - 5xy - 5xy + 25y² = **x² - 10xy + 25y²**

### Using the Square of a Binomial Formula

The formula for squaring a binomial is: (a - b)² = a² - 2ab + b²

In this case, a = x and b = 5y. Substituting these values into the formula:

x² - 2(x)(5y) + (5y)² = **x² - 10xy + 25y²**

### Conclusion

Both methods lead to the same result: **(x - 5y)² = x² - 10xy + 25y²**. It's important to remember that squaring a binomial results in a trinomial (a polynomial with three terms) where the middle term is twice the product of the terms in the binomial.