Expanding the Expression (x+1)(x+8)
This expression represents the product of two binomials. To expand it, we can use the FOIL method, which stands for First, Outer, Inner, Last.
Steps to Expand the Expression:

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: (1) * (x) = x

Last: Multiply the last terms of each binomial: (1) * (8) = 8

Combine all the terms: x² + 8x + x + 8

Simplify by combining like terms: x² + 9x + 8
Therefore, the expanded form of (x+1)(x+8) is x² + 9x + 8.
Understanding the Result
This expanded form is a quadratic expression. It represents a parabola when graphed. The expression can be used in various mathematical applications, such as solving equations, finding roots, or analyzing the behavior of functions.