## Expanding (x + 12)^2 into a Trinomial

The expression (x + 12)^2 represents the square of a binomial. To express this in standard trinomial form, we need to expand it using the distributive property or by recognizing a pattern.

### Using the Distributive Property

We can expand (x + 12)^2 by multiplying it by itself:

(x + 12)^2 = (x + 12)(x + 12)

Now, we can use the distributive property (also known as FOIL) to multiply the terms:

**F**irst: x * x = x^2**O**uter: x * 12 = 12x**I**nner: 12 * x = 12x**L**ast: 12 * 12 = 144

Combining like terms, we get:

x^2 + 12x + 12x + 144 = **x^2 + 24x + 144**

### Using the Pattern

We can also recognize that squaring a binomial follows a specific pattern:

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

In our case, a = x and b = 12. Applying the pattern, we get:

x^2 + 2(x)(12) + 12^2 = **x^2 + 24x + 144**

### Conclusion

Both methods lead us to the same result: (x + 12)^2 expanded in standard trinomial form is **x^2 + 24x + 144**. This form is useful for simplifying expressions, solving equations, and understanding the relationship between different algebraic forms.