To simplify the expression \( 4x^3 - 5x + 5 \times 3x^2 + 6x + 2 \), we need to follow the order of operations: first, multiplication, then addition and subtraction.

### Step-by-step simplification:

1. The given expression is:
   \[
   4x^3 - 5x + 5 \times 3x^2 + 6x + 2
   \]
   
2. First, multiply \( 5 \) and \( 3x^2 \):
   \[
   5 \times 3x^2 = 15x^2
   \]

3. Substitute the result back into the expression:
   \[
   4x^3 - 5x + 15x^2 + 6x + 2
   \]

4. Now, combine like terms where possible. Group \( -5x \) and \( 6x \):
   \[
   -5x + 6x = x
   \]

5. The simplified expression becomes:
   \[
   4x^3 + 15x^2 + x + 2
   \]

### Final answer:
\[
4x^3 + 15x^2 + x + 2
\]

Would you like further details on this or have any questions?

### Related Questions:
1. How do you factor a cubic polynomial?
2. What are the methods for solving polynomial equations?
3. How can you find the roots of a cubic equation?
4. What are like terms in an algebraic expression?
5. How do you apply the distributive property in polynomials?

### Tip:
When simplifying polynomials, always check if you can combine like terms or factor the expression further for easier calculations!

Learn how to simplify the polynomial expression 4x^3 - 5x + 5(3x^2 + 6x + 2) with a clear, step-by-step guide. This process includes multiplying polynomials, combining like terms, and applying the distributive property. Ideal 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