Let's simplify the given expression:

\[
3(5h^2 - 3h^2) - 2(h^2 + 19)
\]

### Step-by-step solution:

1. **Simplify inside the parentheses**:
   - Inside the first set of parentheses: \( 5h^2 - 3h^2 = 2h^2 \).
   - Inside the second set of parentheses: nothing to simplify yet.

   Now, the expression becomes:
   \[
   3(2h^2) - 2(h^2 + 19)
   \]

2. **Distribute the constants**:
   - Multiply \( 3 \) by \( 2h^2 \): \( 3 \times 2h^2 = 6h^2 \).
   - Distribute \( -2 \) to both terms in \( (h^2 + 19) \): 
     \[
     -2 \times h^2 = -2h^2
     \]
     \[
     -2 \times 19 = -38
     \]

   Now the expression is:
   \[
   6h^2 - 2h^2 - 38
   \]

3. **Combine like terms**:
   - Combine \( 6h^2 \) and \( -2h^2 \): 
     \[
     6h^2 - 2h^2 = 4h^2
     \]

   So, the expression simplifies to:
   \[
   4h^2 - 38
   \]

### Final Answer:
\[
4h^2 - 38
\]

Do you have any questions or would you like more details?

Here are 5 related questions to consider:
1. How would you factor the expression \( 4h^2 - 38 \)?
2. How do you solve for \( h \) in the equation \( 4h^2 - 38 = 0 \)?
3. What happens if there are more variables in the expression?
4. How would you differentiate \( 4h^2 - 38 \) with respect to \( h \)?
5. What is the result if you substitute \( h = 2 \) into the simplified expression?

**Tip:** Always check for common factors after simplifying an expression; it can help in further reductions or solving equations.

Simplify 3(5h^2 − 3h^2) − 2(h^2 + 19).

Simplify the polynomial expression 3(5h^2 − 3h^2) − 2(h^2 + 19) with a step-by-step guide. This solution involves using the distributive property and combining like terms. Suitable for students in 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