Expand the expression to a polynomial in standard form:

left parenthesis, 3, x, plus, 2, right parenthesis, left parenthesis, minus, x, squared, minus, 4, x, minus, 6, right parenthesis

(3*x*+2)(−*x*2−4*x*−6)

To expand the expression \((3x + 2)(-x^2 - 4x - 6)\), we'll use the distributive property, also known as the FOIL method for binomials.

### Step 1: Distribute \(3x\) across \(-x^2 - 4x - 6\):
\[
3x \cdot (-x^2) = -3x^3
\]
\[
3x \cdot (-4x) = -12x^2
\]
\[
3x \cdot (-6) = -18x
\]

### Step 2: Distribute \(2\) across \(-x^2 - 4x - 6\):
\[
2 \cdot (-x^2) = -2x^2
\]
\[
2 \cdot (-4x) = -8x
\]
\[
2 \cdot (-6) = -12
\]

### Step 3: Combine all the terms:
\[
-3x^3 - 12x^2 - 18x - 2x^2 - 8x - 12
\]

### Step 4: Combine like terms:
\[
-3x^3 + (-12x^2 - 2x^2) + (-18x - 8x) - 12
\]
\[
-3x^3 - 14x^2 - 26x - 12
\]

### Final Answer:
The expanded polynomial in standard form is:
\[
\boxed{-3x^3 - 14x^2 - 26x - 12}
\]

Would you like any details or have questions on this solution?

Here are some related questions:
1. How do you factor the polynomial \(-3x^3 - 14x^2 - 26x - 12\)?
2. What happens when you expand \((2x - 3)(x^2 + 5x + 6)\)?
3. Can you explain the FOIL method used for binomial expansion?
4. What is the significance of the standard form of a polynomial?
5. How do you identify and combine like terms in polynomial expressions?

**Tip:** When expanding polynomials, always make sure to combine like terms to simplify your final expression.

Learn how to expand the expression (3x + 2)(-x^2 - 4x - 6) into a polynomial in standard form using the FOIL method and combining like terms. This detailed solution covers key algebraic concepts and is suitable for students in Grades 9-12.

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