Factoring and Expanding: (x5)(x+3)
This expression represents the multiplication of two binomials: (x5) and (x+3). Let's explore how to factor and expand it.
Expanding the Expression
To expand the expression, we use the FOIL method:
 First: Multiply the first terms of each binomial: x * x = x²
 Outer: Multiply the outer terms of the binomials: x * 3 = 3x
 Inner: Multiply the inner terms of the binomials: 5 * x = 5x
 Last: Multiply the last terms of each binomial: 5 * 3 = 15
Now, combine the terms:
x² + 3x  5x  15
Simplify by combining like terms:
x²  2x  15
Therefore, the expanded form of (x5)(x+3) is x²  2x  15.
Factoring the Expression
We can also factor the expression x²  2x  15 back into its original binomial form. Here's how:

Find two numbers that multiply to 15 and add up to 2. These numbers are 5 and 3.

Rewrite the expression using these numbers: x²  5x + 3x  15

Factor by grouping: x(x5) + 3(x5)

Factor out the common binomial: (x5)(x+3)
Therefore, the factored form of x²  2x  15 is (x5)(x+3).
Conclusion
Expanding and factoring are important skills in algebra. By understanding the FOIL method and factoring techniques, you can manipulate expressions like (x5)(x+3) to reveal their expanded or factored forms.