Let's expand the expression \((2x + 1)(-3x^2 - 6x - 4)\) step by step.

### Step 1: Distribute each term of the first binomial to every term of the second binomial.

\[
(2x + 1)(-3x^2 - 6x - 4) = 2x(-3x^2 - 6x - 4) + 1(-3x^2 - 6x - 4)
\]

### Step 2: Distribute \(2x\) to each term in the second binomial:

\[
2x(-3x^2) + 2x(-6x) + 2x(-4) = -6x^3 - 12x^2 - 8x
\]

### Step 3: Distribute \(1\) to each term in the second binomial:

\[
1(-3x^2) + 1(-6x) + 1(-4) = -3x^2 - 6x - 4
\]

### Step 4: Combine all the terms together:

\[
-6x^3 - 12x^2 - 8x - 3x^2 - 6x - 4
\]

### Step 5: Combine like terms:

\[
-6x^3 + (-12x^2 - 3x^2) + (-8x - 6x) - 4 = -6x^3 - 15x^2 - 14x - 4
\]

### Final Answer:
\[
\boxed{-6x^3 - 15x^2 - 14x - 4}
\]

Would you like any further explanation or details?

---

Here are 8 related questions you might find useful:

1. How do you factor a cubic polynomial like \(-6x^3 - 15x^2 - 14x - 4\)?
2. What are the roots of the polynomial \(-6x^3 - 15x^2 - 14x - 4\)?
3. What is the process of expanding polynomials using the distributive property?
4. How do you simplify negative coefficients in polynomial expansion?
5. What are common errors when expanding expressions involving negative signs?
6. How do you identify and combine like terms in a polynomial?
7. How can polynomial division be used to simplify expressions?
8. What are the differences between monomials, binomials, and polynomials?

**Tip:** Always pay special attention to the signs of terms when distributing and combining like terms, as it's easy to make errors with negative signs.

Learn how to expand the expression (2x + 1)(-3x^2 - 6x - 4) with detailed steps and examples. This problem involves applying the distributive property of multiplication over addition and subtraction in algebra, suitable for Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation