To simplify the expression \(5mx + 10mx - 70m\), we need to combine like terms. The terms \(5mx\) and \(10mx\) are like terms since they both contain \(mx\). Here's how you can simplify the expression step-by-step:

1. **Combine like terms:**  
   - Add the coefficients of the like terms \(5mx\) and \(10mx\):
     \[
     5mx + 10mx = (5 + 10)mx = 15mx
     \]
   
2. **Rewrite the expression:**  
   - After combining the like terms, the expression becomes:
     \[
     15mx - 70m
     \]

3. **Factor the expression (optional):**  
   - If further factorization is desired, factor out the greatest common factor from the entire expression. In this case, \(m\) is a common factor:
     \[
     15mx - 70m = m(15x - 70)
     \]
   - Further simplify the expression inside the parentheses if possible:
     \[
     15x - 70 = 15(x - \frac{70}{15})
     \]
     Since \(\frac{70}{15}\) does not simplify to an integer, the expression is fully simplified as \(m(15x - 70)\).

Thus, the simplified expression is \(15mx - 70m\), or if factoring is needed, \(m(15x - 70)\).

### Do you have any questions or need more details?

Here are some related questions for further exploration:

1. How do you identify like terms in an algebraic expression?
2. What are the common techniques for factoring algebraic expressions?
3. How do you determine the greatest common factor in a polynomial?
4. What is the significance of simplifying algebraic expressions?
5. How can expressions be further simplified or factored in the context of equations?
6. What are the benefits of factoring an expression in solving equations?
7. How can understanding algebraic expressions help in real-world problem-solving?
8. What is the role of coefficients in algebraic expressions?

**Tip:** When simplifying expressions, always look for common factors and like terms to combine or factor out for simplification.

Learn how to simplify the algebraic expression 5mx + 10mx - 70m with a detailed step-by-step guide. This problem covers key algebraic concepts such as combining like terms and factoring. Suitable for Grades 7-9 students and anyone learning algebraic simplification.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation