## Expanding (x+2y)²

The expression (x+2y)² represents the square of the binomial (x+2y). To expand 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**. It's a way to remember how to multiply two binomials.

**First:**Multiply the first terms of each binomial: x * x = x²**Outer:**Multiply the outer terms of the binomials: x * 2y = 2xy**Inner:**Multiply the inner terms of the binomials: 2y * x = 2xy**Last:**Multiply the last terms of each binomial: 2y * 2y = 4y²

Now, add all the terms together: x² + 2xy + 2xy + 4y²

Combining like terms, we get: **x² + 4xy + 4y²**

### Using the Square of a Binomial Formula

The square of a binomial formula states: (a + b)² = a² + 2ab + b²

In our case, a = x and b = 2y. Applying the formula:

(x + 2y)² = x² + 2(x)(2y) + (2y)²

Simplifying, we get: **x² + 4xy + 4y²**

### Conclusion

Both methods, the FOIL method and the square of a binomial formula, lead to the same answer. The expanded form of (x+2y)² is **x² + 4xy + 4y²**. This expression represents a **trinomial** with three terms: a squared term (x²), a linear term (4xy), and a squared term (4y²).