36mn(25m square-49 n square ÷4mn(5m+7n divide the following y the method of factorsisation

To solve the expression \(\frac{36mn(25m^2 - 49n^2)}{4mn(5m + 7n)}\) by the method of factorization, we'll go step by step.

### Step 1: Factorize the numerator and denominator
The given expression is:

\[
\frac{36mn(25m^2 - 49n^2)}{4mn(5m + 7n)}
\]

1. **Factorizing \(25m^2 - 49n^2\)**:  
   This is a difference of squares, which can be factored as:

   \[
   25m^2 - 49n^2 = (5m - 7n)(5m + 7n)
   \]

   So the numerator becomes:

   \[
   36mn \cdot (5m - 7n)(5m + 7n)
   \]

2. **Simplify the expression**:

   The full expression now is:

   \[
   \frac{36mn \cdot (5m - 7n)(5m + 7n)}{4mn \cdot (5m + 7n)}
   \]

### Step 2: Cancel out the common factors
- \(36mn\) and \(4mn\) have common factors:
  \[
  \frac{36mn}{4mn} = 9
  \]

- \((5m + 7n)\) in the numerator and denominator cancel out:
  \[
  \frac{(5m + 7n)}{(5m + 7n)} = 1
  \]

Thus, the simplified expression is:

\[
9(5m - 7n)
\]

### Final Answer:
The simplified expression is:

\[
9(5m - 7n)
\]

Would you like any further details or explanations?

---

Here are some related questions you might find useful:
1. What is the difference of squares method?
2. How do you factor a quadratic expression?
3. Can you always cancel out terms in a fraction?
4. What are the common mistakes to avoid in factorization?
5. How do you simplify expressions involving multiple variables?
6. What is the role of the distributive property in algebra?
7. How can you factor a trinomial?
8. What is the difference between factoring and expanding an expression?

**Tip:** Always look for common factors first when simplifying algebraic expressions. This can save time and prevent errors.

Explore how to factorize the algebraic expression 36mn(25m^2 - 49n^2) / 4mn(5m + 7n) step-by-step. This problem involves algebraic factorization, specifically using the difference of squares method. 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