https://file.aiquickdraw.com/mathbot/file/1725364890776uvfj6tfb.jpg

The expression in the image is:

\[
(5x^3 - 3) - (-4x^3 + 8)
\]

We are also told that this expression is equivalent to \( bx^3 - 11 \), and we need to find the value of \( b \), where \( b \) is a constant.

### Step 1: Simplify the given expression
First, expand the expression:
\[
(5x^3 - 3) - (-4x^3 + 8) = 5x^3 - 3 + 4x^3 - 8
\]

Now combine like terms:
\[
(5x^3 + 4x^3) + (-3 - 8) = 9x^3 - 11
\]

### Step 2: Compare with the given equivalent expression
The simplified expression \( 9x^3 - 11 \) is equivalent to \( bx^3 - 11 \). By comparing coefficients, we can see that:
\[
b = 9
\]

### Final Answer:
The value of \( b \) is \( \boxed{9} \).

Would you like more details, or do you have any questions?

Here are five related questions for practice:
1. How would you solve for \( b \) if the given expression included higher powers of \( x \)?
2. What happens if the expression on the right-hand side includes an additional constant term?
3. Can you find the value of \( b \) if the expression on the left-hand side was multiplied by a constant factor?
4. How would you approach solving if the expression was quadratic instead of cubic?
5. What method would you use to solve for multiple constants if the expression involved multiple variables?

**Tip:** When simplifying algebraic expressions, carefully expand terms and combine like terms to avoid common mistakes.

Learn how to simplify and solve the polynomial expression 5x^3 - 3 - (-4x^3 + 8) step-by-step with a detailed solution. This problem involves algebraic simplification and finding the value of a constant term. 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