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

This expression represents the product of three binomials. To understand it better, we can expand it step by step.

### Step 1: Expanding the first two binomials

First, we expand (x+6)(x-1) using the **FOIL method**:

**F**irst: x * x = x²**O**uter: x * -1 = -x**I**nner: 6 * x = 6x**L**ast: 6 * -1 = -6

Combining the terms, we get:

(x+6)(x-1) = x² -x + 6x -6 = **x² + 5x - 6**

### Step 2: Expanding the result with the third binomial

Now, we multiply the result from step 1 (x² + 5x - 6) with (x-2):

We can use the **distributive property** to do this:

**x² * (x-2) = x³ - 2x²****5x * (x-2) = 5x² - 10x****-6 * (x-2) = -6x + 12**

Combining all the terms, we get:

(x² + 5x - 6)(x-2) = x³ - 2x² + 5x² - 10x - 6x + 12

Finally, simplifying by combining like terms:

**(x+6)(x-1)(x-2) = x³ + 3x² - 16x + 12**

### Conclusion

Therefore, the expanded and simplified form of (x+6)(x-1)(x-2) is **x³ + 3x² - 16x + 12**. This expression represents a cubic polynomial with a leading coefficient of 1.