Simplity: `(x-6) (x-4) (x+2)`

Answer

To simplify the expression \((x-6)(x-4)(x+2)\), we will follow these steps:

### Step 1: Multiply the first two factors
We start by multiplying the first two brackets: \((x-6)\) and \((x-4)\).

\[ (x-6)(x-4) = x^2 - 4x - 6x + 24 = x^2 - 10x + 24 \]

### Step 2: Multiply the result with the third factor
Now, we take the result from Step 1, which is \((x^2 - 10x + 24)\), and multiply it by the third factor \((x+2)\).

\[ (x^2 - 10x + 24)(x + 2) \]

We will distribute each term in \((x^2 - 10x + 24)\) by \((x + 2)\):

1. Multiply \(x^2\) by \((x + 2)\):
\[ x^2 \cdot x + x^2 \cdot 2 = x^3 + 2x^2 \]

2. Multiply \(-10x\) by \((x + 2)\):
\[ -10x \cdot x - 10x \cdot 2 = -10x^2 - 20x \]

3. Multiply \(24\) by \((x + 2)\):
\[ 24 \cdot x + 24 \cdot 2 = 24x + 48 \]

### Step 3: Combine all the terms
Now, we combine all the terms from the above multiplications:

\[ x^3 + 2x^2 - 10x^2 - 20x + 24x + 48 \]

Combine like terms:

- For \(x^2\) terms: \(2x^2 - 10x^2 = -8x^2\)
- For \(x\) terms: \(-20x + 24x = 4x\)

So, we have:

\[ x^3 - 8x^2 + 4x + 48 \]

### Final Result
Thus, the simplified expression is:

\[ \boxed{x^3 - 8x^2 + 4x + 48} \]

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