To simplify the given expression \( 5h^4 - \frac{3h^3(3h + 4h^2)}{2h^2} \), we need to perform the following steps:

1. Distribute and simplify within the parentheses.
2. Simplify the fractions.
3. Combine like terms if possible.

Let's break it down step-by-step.

### Step 1: Simplify the expression within the parentheses
\[
3h + 4h^2
\]

### Step 2: Multiply the result by \( 3h^3 \)
\[
3h^3 (3h + 4h^2) = 3h^3 \cdot 3h + 3h^3 \cdot 4h^2 = 9h^4 + 12h^5
\]

### Step 3: Divide by \( 2h^2 \)
\[
\frac{9h^4 + 12h^5}{2h^2}
\]
Divide each term by \( 2h^2 \):
\[
= \frac{9h^4}{2h^2} + \frac{12h^5}{2h^2} = \frac{9}{2}h^2 + 6h^3
\]

### Step 4: Combine with the original term
Now, combine the simplified term with \( 5h^4 \):
\[
5h^4 - \left( \frac{9}{2}h^2 + 6h^3 \right)
\]

### Step 5: Write the final simplified expression
\[
= 5h^4 - \frac{9}{2}h^2 - 6h^3
\]

Therefore, the simplified expression is:
\[
5h^4 - 6h^3 - \frac{9}{2}h^2
\]

Would you like more details or have any questions?

Here are 5 questions you can ask next:
1. How do you simplify rational expressions?
2. What are the steps to factor a polynomial?
3. How do you solve quadratic equations?
4. Can you explain the process of polynomial division?
5. How do you find the derivative of a function?

**Tip:** Always perform operations step-by-step to avoid mistakes and ensure each part of the expression is simplified correctly.

Learn how to simplify the polynomial expression 5h^4 - 3h^3(3h + 4h^2)/2h^2 step-by-step. This problem involves algebraic manipulation of polynomials and fractional expressions. Suitable 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