## Simplifying (x + 4)^2

The expression (x + 4)^2 represents the square of the binomial (x + 4). To simplify this, 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 two binomials together. Here's how it works:

**First:**Multiply the first terms of each binomial: x * x = x^2**Outer:**Multiply the outer terms of the binomials: x * 4 = 4x**Inner:**Multiply the inner terms of the binomials: 4 * x = 4x**Last:**Multiply the last terms of each binomial: 4 * 4 = 16

Now, we add all the terms together: x^2 + 4x + 4x + 16

Combining like terms, we get:

**(x + 4)^2 = x^2 + 8x + 16**

### Using the Square of a Binomial Pattern

The square of a binomial pattern states:

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

In our case, a = x and b = 4. Substituting these values into the pattern, we get:

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

Simplifying, we get:

**(x + 4)^2 = x^2 + 8x + 16**

### Conclusion

Therefore, both the FOIL method and the square of a binomial pattern lead to the simplified expression: **(x + 4)^2 = x^2 + 8x + 16**. Remember, understanding these methods helps you simplify similar expressions and solve equations efficiently.