## Expanding the Expression: (d+6)(2d^2-d+7)

This expression represents the product of two polynomials: a binomial (d+6) and a trinomial (2d^2-d+7). To simplify this expression, we will use the distributive property, commonly known as **FOIL** (First, Outer, Inner, Last).

### Using FOIL to Expand

**1. First:** Multiply the first terms of each polynomial:

- d * 2d^2 =
**2d^3**

**2. Outer:** Multiply the outer terms of each polynomial:

- d * 7 =
**7d**

**3. Inner:** Multiply the inner terms of each polynomial:

- 6 * 2d^2 =
**12d^2**

**4. Last:** Multiply the last terms of each polynomial:

- 6 * -d =
**-6d** - 6 * 7 =
**42**

### Combining the Terms

Now, we combine all the terms we obtained:

2d^3 + 7d + 12d^2 - 6d + 42

Finally, we arrange the terms in descending order of their exponents:

**2d^3 + 12d^2 + d + 42**