## Expanding (x + 4y)^2

The expression (x + 4y)^2 represents the square of a binomial. To expand it, we can use the **FOIL** method or the **square of a binomial formula**.

### Using FOIL

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

Here's how it works for (x + 4y)^2:

**First**: x * x = x^2**Outer**: x * 4y = 4xy**Inner**: 4y * x = 4xy**Last**: 4y * 4y = 16y^2

Now, combine the terms: x^2 + 4xy + 4xy + 16y^2

Finally, simplify by combining like terms: **x^2 + 8xy + 16y^2**

### Using the Square of a Binomial Formula

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

Applying this to our expression, we have:

(x + 4y)^2 = x^2 + 2(x)(4y) + (4y)^2

Simplifying: **x^2 + 8xy + 16y^2**

### Conclusion

Both methods lead to the same expanded form of (x + 4y)^2: **x^2 + 8xy + 16y^2**. Choose the method that you find easier to understand and apply.