## Expanding (x + 12)^2

The expression (x + 12)^2 represents the square of the binomial (x + 12). 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**, and it's a way to multiply two binomials.

**First:**Multiply the**first**terms of each binomial: x * x = x^2**Outer:**Multiply the**outer**terms of the binomials: x * 12 = 12x**Inner:**Multiply the**inner**terms of the binomials: 12 * x = 12x**Last:**Multiply the**last**terms of each binomial: 12 * 12 = 144

Now, combine the terms: x^2 + 12x + 12x + 144

Simplify by combining the like terms:
**x^2 + 24x + 144**

### Using the Square of a Binomial Formula

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

In this case, a = x and b = 12.

Applying the formula: (x + 12)^2 = x^2 + 2(x)(12) + 12^2

Simplifying:
**x^2 + 24x + 144**

### Conclusion

Both methods lead to the same expanded form of (x + 12)^2, which is **x^2 + 24x + 144**. You can choose whichever method you find easier to apply. Understanding these methods will be helpful for expanding other binomial expressions and solving various algebraic problems.