## Expanding the Square: Solving (x + 2y)²

The expression (x + 2y)² represents the square of a binomial. To solve this, we need to expand it using the distributive property or the FOIL method.

**Understanding the Formula:**

The formula for squaring a binomial is:

**(a + b)² = a² + 2ab + b²**

**Applying the Formula:**

**Identify a and b:**In our case, a = x and b = 2y.**Substitute into the formula:**(x + 2y)² = x² + 2(x)(2y) + (2y)²**Simplify:**(x + 2y)² =**x² + 4xy + 4y²**

**Therefore, the solution to (x + 2y)² is x² + 4xy + 4y².**

**Key Points:**

**FOIL Method:**You can also expand the expression using the FOIL method (First, Outer, Inner, Last).**Visualizing the Solution:**Think of (x + 2y)² as (x + 2y) multiplied by itself. When you visualize this multiplication, you can see how each term in the expansion is formed.

**Remember:** Always simplify your answer by combining like terms.