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 problems one by one using the distributive property.

### 6. \(-6x (2x - 3x^2 + 7)\)

Distribute \(-6x\) across each term inside the parentheses:
\[
-6x(2x) = -12x^2
\]
\[
-6x(-3x^2) = 18x^3
\]
\[
-6x(7) = -42x
\]

So, the result is:
\[
18x^3 - 12x^2 - 42x
\]

---

### 7. \(8x (3x^3 + 2x^2 - 4x + 5)\)

Distribute \(8x\) across each term:
\[
8x(3x^3) = 24x^4
\]
\[
8x(2x^2) = 16x^3
\]
\[
8x(-4x) = -32x^2
\]
\[
8x(5) = 40x
\]

So, the result is:
\[
24x^4 + 16x^3 - 32x^2 + 40x
\]

---

### 8. \(-3x (4x^2 + 6x - 1)\)

Distribute \(-3x\) across each term:
\[
-3x(4x^2) = -12x^3
\]
\[
-3x(6x) = -18x^2
\]
\[
-3x(-1) = 3x
\]

So, the result is:
\[
-12x^3 - 18x^2 + 3x
\]

---

### 9. \(2x (7x^3 - 2x^2 + x - 8)\)

Distribute \(2x\) across each term:
\[
2x(7x^3) = 14x^4
\]
\[
2x(-2x^2) = -4x^3
\]
\[
2x(x) = 2x^2
\]
\[
2x(-8) = -16x
\]

So, the result is:
\[
14x^4 - 4x^3 + 2x^2 - 16x
\]

---

### 10. \(-4x (3x^2 - 5x + 9)\)

Distribute \(-4x\) across each term:
\[
-4x(3x^2) = -12x^3
\]
\[
-4x(-5x) = 20x^2
\]
\[
-4x(9) = -36x
\]

So, the result is:
\[
-12x^3 + 20x^2 - 36x
\]

---

Would you like any further details or explanations on these steps?

Here are 

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) =

Learn how to solve polynomial expressions using the distributive property. This step-by-step guide covers examples like -6x(2x - 3x^2 + 7) and 8x(3x^3 + 2x^2 - 4x + 5), breaking down the distributive property with polynomials. Ideal for students in Grades 8-10.

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