Expanding (x+5)(x+4)
The expression (x+5)(x+4) 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 describes the order in which we multiply the terms of the binomials.
Here's how to apply the FOIL method:

First: Multiply the first terms of each binomial: x * x = x²

Outer: Multiply the outer terms of the binomials: x * 4 = 4x

Inner: Multiply the inner terms of the binomials: 5 * x = 5x

Last: Multiply the last terms of the binomials: 5 * 4 = 20
Now, we have all the individual products. Combine them to get the final expanded expression:
(x+5)(x+4) = x² + 4x + 5x + 20
Finally, combine the like terms (4x and 5x):
(x+5)(x+4) = x² + 9x + 20
Therefore, the expanded form of (x+5)(x+4) is x² + 9x + 20.
Understanding the FOIL Method
The FOIL method is a visual and organized way to multiply binomials. It ensures that every term in the first binomial is multiplied by every term in the second binomial. This method is especially helpful when dealing with more complex binomials or when working with polynomials with multiple terms.