## Expanding (x+3)^2 into a Trinomial

The expression (x+3)^2 represents the square of the binomial (x+3). To expand this expression into a trinomial in standard form, we can use the **FOIL method** or the **square of a binomial formula**.

### Using the FOIL Method

**FOIL** stands for **First, Outer, Inner, Last**, which describes the order in which we multiply the terms of the binomials.

**First:**Multiply the first terms of each binomial: x * x = x^2**Outer:**Multiply the outer terms of the binomials: x * 3 = 3x**Inner:**Multiply the inner terms of the binomials: 3 * x = 3x**Last:**Multiply the last terms of each binomial: 3 * 3 = 9

Now we add all the products together: x^2 + 3x + 3x + 9

Finally, combine the like terms:
**x^2 + 6x + 9**

### Using the Square of a Binomial Formula

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

In our case, a = x and b = 3. Applying the formula:

x^2 + 2(x)(3) + 3^2

Simplifying the expression:
**x^2 + 6x + 9**

### Conclusion

Both methods lead to the same result: **(x+3)^2 expands to the trinomial x^2 + 6x + 9 in standard form.**