## Expanding and Simplifying (x+2)(x−1)(2x+1)(x+6)

This article explores how to expand and simplify the given expression: **(x+2)(x−1)(2x+1)(x+6)**. We'll utilize the distributive property and combine like terms to arrive at a simplified polynomial form.

### Step 1: Expand the first two factors.

First, we'll multiply the first two factors, (x+2)(x−1) using the **FOIL** method (First, Outer, Inner, Last):

(x+2)(x−1) = x² - x + 2x - 2 = x² + x - 2

### Step 2: Expand the last two factors.

Similarly, we'll multiply the last two factors, (2x+1)(x+6):

(2x+1)(x+6) = 2x² + 12x + x + 6 = 2x² + 13x + 6

### Step 3: Expand the resulting expressions.

Now, we have the expression: **(x² + x - 2)(2x² + 13x + 6)**. Let's expand this by multiplying each term in the first expression by each term in the second expression.

**x² * (2x² + 13x + 6)** = 2x⁴ + 13x³ + 6x²
**x * (2x² + 13x + 6)** = 2x³ + 13x² + 6x
**-2 * (2x² + 13x + 6)** = -4x² - 26x - 12

### Step 4: Combine like terms.

Finally, we add all the resulting terms together and combine like terms:

2x⁴ + 13x³ + 6x² + 2x³ + 13x² + 6x - 4x² - 26x - 12

= **2x⁴ + 15x³ + 15x² - 20x - 12**

Therefore, the simplified form of the expression **(x+2)(x−1)(2x+1)(x+6)** is **2x⁴ + 15x³ + 15x² - 20x - 12**.