Training Camp (cont 11)

Watch the video to see more examples of Multiplying Binomials

Now that you have reviewed multiplying binomials, you can carry on with the next part of this lesson. The multiplying you reviewed will be used at the end of Examples 8 and 9.

To simplify an algebraic expression involving factorials, three key concepts will be applied.

• The ellipsis (...) is used to represent the middle portion of a factorial in expanded form.

• (3) × (2) × (1) is always at the end of a factorial in expanded form because every string of natural numbers ends in 3, 2, 1.

• A factorial is the product of consecutive descending natural numbers. In other words, each number in expanded form is one less than the number before it.

How can you show consecutive and descending using algebraic expressions? Assume the initial number in the factorial is represented by ( n + 2). You can show the number that is exactly one less than this by subtracting one .

You can continue this pattern as needed to simplify the factorial.

Using this information, you can write ( n + 2)! in expanded form:

( n + 2)! = ( n + 2) × ( n + 1) × ( n ) × ( n - 1) × ( n - 2) × ... × 3 × 2 × 1