We need to distribute the \(-6w^4\) to both terms inside the parentheses \((-9w^2 + 4w)\). Let's go step by step.

### Step 1: Distribute \(-6w^4\) to \(-9w^2\)
\[
-6w^4 \times -9w^2 = 54w^{6}
\]
Multiplying the coefficients gives \(54\), and using the laws of exponents \((w^4 \times w^2 = w^{6})\).

### Step 2: Distribute \(-6w^4\) to \(4w\)
\[
-6w^4 \times 4w = -24w^5
\]
Multiplying the coefficients gives \(-24\), and using the laws of exponents \((w^4 \times w = w^{5})\).

### Final Expression:
\[
54w^6 - 24w^5
\]

This is the simplified expression after distribution.

Would you like a more detailed explanation, or do you have any further questions?

Here are 5 related questions to explore:
1. What is the general rule for distributing variables with exponents?
2. How do you add or subtract exponents in multiplication?
3. Can you simplify \((3w^3)(-2w^4 + 5w^2)\)?
4. What happens when you distribute over a polynomial with three terms?
5. How would the problem change if one of the terms inside the parentheses had a negative exponent?

**Tip:** Always remember to follow the laws of exponents when distributing terms involving variables with powers.

Learn how to simplify the polynomial expression -6w^4(-9w^2+4w) using the distribution method and the laws of exponents. This step-by-step solution covers key algebraic concepts, including distributing polynomials and exponent rules. Ideal for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation