## Expanding (d + 3)^2

The expression **(d + 3)^2** represents the square of the binomial (d + 3). To expand this expression, we can use the **FOIL** method or the **square of a binomial** formula.

### Using the FOIL Method

**F**irst: Multiply the first terms of each binomial:**d * d = d^2****O**uter: Multiply the outer terms of the binomials:**d * 3 = 3d****I**nner: Multiply the inner terms of the binomials:**3 * d = 3d****L**ast: Multiply the last terms of each binomial:**3 * 3 = 9**

Adding all the results together: **d^2 + 3d + 3d + 9**

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

### Using the Square of a Binomial Formula

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

Applying this to our expression:

- a = d
- b = 3

Substituting the values: **d^2 + 2(d)(3) + 3^2**

Simplifying: **d^2 + 6d + 9**

Therefore, the expanded form of **(d + 3)^2** is **d^2 + 6d + 9**.