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

The expression (x + 12)^2 represents the square of the binomial (x + 12). To expand it as a trinomial, we can utilize the **FOIL** method or the **square of a binomial** formula.

### Using the FOIL Method

FOIL stands for **First, Outer, Inner, Last**. This method helps us multiply two binomials. Let's apply it to (x + 12)^2:

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

Now, add all the results together:

x^2 + 12x + 12x + 144

Combining like terms:

**x^2 + 24x + 144**

Therefore, (x + 12)^2 expanded as a trinomial is **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

Applying this formula to (x + 12)^2, where a = x and b = 12:

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

Simplifying:

**x^2 + 24x + 144**

Both methods lead to the same result: **(x + 12)^2 = x^2 + 24x + 144**.

This trinomial represents the expanded form of the squared binomial.