## Factoring and Simplifying the Expression: (p^2 + p - 6)(p^2 - 6)

This expression involves the multiplication of two quadratic expressions. To simplify it, we can use the following steps:

### Step 1: Factor each quadratic expression

**(p^2 + p - 6)**can be factored as**(p + 3)(p - 2)**. To factor this, we need to find two numbers that multiply to -6 and add up to 1 (the coefficient of the middle term). The numbers 3 and -2 satisfy these conditions.**(p^2 - 6)**cannot be factored further as it's a difference of squares.

### Step 2: Multiply the factored expressions

Now we have: **(p + 3)(p - 2)(p^2 - 6)**

### Step 3: Expanding the expression (optional)

While the expression is simplified by factoring, we can further expand it by multiplying the terms:

**(p + 3)(p - 2)(p^2 - 6) = (p^3 - 2p^2 + 3p^2 - 6p)(p^2 - 6)**
= **(p^3 + p^2 - 6p)(p^2 - 6)**
= **p^5 - 6p^3 + p^4 - 6p^2 - 6p^3 + 36p**
= **p^5 + p^4 - 12p^3 - 6p^2 + 36p**

**Therefore, the simplified form of (p^2 + p - 6)(p^2 - 6) is (p + 3)(p - 2)(p^2 - 6), or in expanded form, p^5 + p^4 - 12p^3 - 6p^2 + 36p.**