6.  -6x (2x - 3x2 + 7) =                     

7.  8x (3x3 + 2x2 - 4x + 5) =            

8.  -3x (4x2 + 6x - 1) =                     

9.  2x (7x3 - 2x2 + x - 8) =                

10.  -4x (3x2 - 5x + 9) =       

Let’s solve each of these expressions by applying the distributive property, which involves multiplying the term outside the parentheses by each term inside the parentheses.

### 6. \(-6x(2x - 3x^2 + 7)\)
\[
-6x(2x - 3x^2 + 7) = (-6x \cdot 2x) + (-6x \cdot -3x^2) + (-6x \cdot 7)
\]
\[
= -12x^2 + 18x^3 - 42x
\]
So, the solution is:
\[
18x^3 - 12x^2 - 42x
\]

### 7. \(8x(3x^3 + 2x^2 - 4x + 5)\)
\[
8x(3x^3 + 2x^2 - 4x + 5) = (8x \cdot 3x^3) + (8x \cdot 2x^2) + (8x \cdot -4x) + (8x \cdot 5)
\]
\[
= 24x^4 + 16x^3 - 32x^2 + 40x
\]
So, the solution is:
\[
24x^4 + 16x^3 - 32x^2 + 40x
\]

### 8. \(-3x(4x^2 + 6x - 1)\)
\[
-3x(4x^2 + 6x - 1) = (-3x \cdot 4x^2) + (-3x \cdot 6x) + (-3x \cdot -1)
\]
\[
= -12x^3 - 18x^2 + 3x
\]
So, the solution is:
\[
-12x^3 - 18x^2 + 3x
\]

### 9. \(2x(7x^3 - 2x^2 + x - 8)\)
\[
2x(7x^3 - 2x^2 + x - 8) = (2x \cdot 7x^3) + (2x \cdot -2x^2) + (2x \cdot x) + (2x \cdot -8)
\]
\[
= 14x^4 - 4x^3 + 2x^2 - 16x
\]
So, the solution is:
\[
14x^4 - 4x^3 + 2x^2 - 16x
\]

### 10. \(-4x(3x^2 - 5x + 9)\)
\[
-4x(3x^2 - 5x + 9) = (-4x \cdot 3x^2) + (-4x \cdot -5x) + (-4x \cdot 9)
\]
\[
= -12x^3 + 20x^2 - 36x
\]
So, the solution is:
\[
-12x^3 + 20x^2 - 36x
\]

---

Would you like more details or explanations on any of the steps?

Here are some related questions:
1. How does the distributive property work with negative coefficients?
2. What happens when you multiply two terms with exponents?
3. How do you simplify expressions after distributing terms?
4. How does the degree of the polynomial change after distributing?
5. What are common mistakes to avoid in distribution?

**Tip:** Always double-check signs when distributing negative coefficients to avoid errors!

6. -6x (2x - 3x^2 + 7) = 
7. 8x (3x^3 + 2x^2 - 4x + 5) = 
8. -3x (4x^2 + 6x - 1) = 
9. 2x (7x^3 - 2x^2 + x - 8) = 
10. -4x (3x^2 - 5x + 9) =

Explore how to apply the distributive property to polynomial expressions such as -6x(2x - 3x^2 + 7) and 8x(3x^3 + 2x^2 - 4x + 5). This guide provides a detailed step-by-step solution, covering key algebraic concepts for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation