## Expanding (x+1)(x+8)

In mathematics, expanding an expression often involves using the distributive property. This property states that multiplying a sum by a number is the same as multiplying each term of the sum by that number. Let's apply this to the expression (x+1)(x+8):

### Using the FOIL method

The **FOIL** method is a mnemonic device used to remember the order of multiplication when expanding two binomials:

**F**irst: Multiply the first terms of each binomial: x * x =**x²****O**uter: Multiply the outer terms of the binomials: x * 8 =**8x****I**nner: Multiply the inner terms of the binomials: 1 * x =**x****L**ast: Multiply the last terms of each binomial: 1 * 8 =**8**

Combining these terms, we get:

(x+1)(x+8) = x² + 8x + x + 8

### Simplifying the Expression

Now we can combine the like terms:

x² + 8x + x + 8 = **x² + 9x + 8**

### Conclusion

Therefore, the expanded form of (x+1)(x+8) is **x² + 9x + 8**.