## Expanding the Expression (x+2)(x+8)

The expression (x+2)(x+8) represents the product of two binomials. To expand this expression, we can use the **FOIL** method. FOIL stands for **First, Outer, Inner, Last**, and it helps us systematically multiply the terms of the binomials.

### Steps to Expand using FOIL

**First:**Multiply the**first**terms of each binomial: x * x =**x²****Outer:**Multiply the**outer**terms of the binomials: x * 8 =**8x****Inner:**Multiply the**inner**terms of the binomials: 2 * x =**2x****Last:**Multiply the**last**terms of the binomials: 2 * 8 =**16**

Now we have: x² + 8x + 2x + 16

### Combining Like Terms

The final step is to combine the like terms, which are the terms with the same variable and exponent:

x² + 8x + 2x + 16 = **x² + 10x + 16**

### Conclusion

Therefore, the expanded form of the expression (x+2)(x+8) is **x² + 10x + 16**. This expression represents a quadratic equation, which can be used to solve for the value of x.