## Expanding (x+15)^2

The expression (x+15)^2 represents the square of the binomial (x+15). To expand this expression, we can use the **FOIL method** or the **square of a binomial pattern**.

### Using the FOIL Method

FOIL stands for **First, Outer, Inner, Last**. This method helps us multiply each term of the first binomial with each term of the second binomial:

**First:**x * x = x^2**Outer:**x * 15 = 15x**Inner:**15 * x = 15x**Last:**15 * 15 = 225

Combining the terms, we get:

**(x+15)^2 = x^2 + 15x + 15x + 225**

Simplifying the expression:

**(x+15)^2 = x^2 + 30x + 225**

### Using the Square of a Binomial Pattern

The square of a binomial pattern states:

**(a + b)^2 = a^2 + 2ab + b^2**

Applying this pattern to our expression:

**(x+15)^2 = x^2 + 2(x)(15) + 15^2**

Simplifying:

**(x+15)^2 = x^2 + 30x + 225**

### Conclusion

Both methods result in the same expanded expression: **x^2 + 30x + 225**. This expanded form is a **trinomial** with a leading coefficient of 1, a linear coefficient of 30, and a constant term of 225. It's important to remember that expanding a squared binomial often simplifies the expression and makes it easier to work with in further calculations or analysis.