## Expanding and Simplifying (5x - 9)^2

The expression (5x - 9)^2 represents the square of the binomial (5x - 9). To simplify this expression, we can use the **FOIL** method or the **square of a binomial** formula.

### Using the FOIL Method

FOIL stands for **First, Outer, Inner, Last**. This method involves multiplying each term of the first binomial by each term of the second binomial:

**First:**(5x) * (5x) = 25x^2**Outer:**(5x) * (-9) = -45x**Inner:**(-9) * (5x) = -45x**Last:**(-9) * (-9) = 81

Adding all the terms together, we get:

**(5x - 9)^2 = 25x^2 - 45x - 45x + 81**

Finally, combining like terms, we have:

**(5x - 9)^2 = 25x^2 - 90x + 81**

### Using the Square of a Binomial Formula

The square of a binomial formula states: **(a - b)^2 = a^2 - 2ab + b^2**

Applying this formula to our expression:

**(5x - 9)^2 = (5x)^2 - 2(5x)(9) + (-9)^2**

Simplifying:

**(5x - 9)^2 = 25x^2 - 90x + 81**

### Conclusion

Both the FOIL method and the square of a binomial formula lead to the same simplified expression: **25x^2 - 90x + 81**. This represents the expanded form of (5x - 9)^2.