## Expanding the Expression (x+3)(x+6)

This expression represents the product of two binomials: (x+3) and (x+6). To find the answer, we need to expand the expression using the distributive property or the FOIL method.

### Using the Distributive Property

The distributive property states that a(b+c) = ab + ac. We can apply this to our expression:

**Step 1:**Distribute the first term of the first binomial (x) over the second binomial: x(x+6) = x² + 6x**Step 2:**Distribute the second term of the first binomial (3) over the second binomial: 3(x+6) = 3x + 18**Step 3:**Combine the results from steps 1 and 2: (x+3)(x+6) = x² + 6x + 3x + 18**Step 4:**Simplify by combining like terms: (x+3)(x+6) =**x² + 9x + 18**

### Using the FOIL Method

FOIL stands for First, Outer, Inner, Last. This method helps remember the order of multiplication when expanding two binomials.

**F:**Multiply the**first**terms of each binomial: x * x = x²**O:**Multiply the**outer**terms: x * 6 = 6x**I:**Multiply the**inner**terms: 3 * x = 3x**L:**Multiply the**last**terms: 3 * 6 = 18**Combine:**x² + 6x + 3x + 18 =**x² + 9x + 18**

### Conclusion

Therefore, the expanded form of the expression (x+3)(x+6) is **x² + 9x + 18**. Both the distributive property and the FOIL method lead to the same answer.