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The expression given in the image is \( 81m^2 - 25n^2 \), and we are told that one of the factors is \( 9m + 5n \). This expression is a difference of squares.

The difference of squares formula is:
\[
a^2 - b^2 = (a - b)(a + b)
\]
In this case, we can rewrite \( 81m^2 - 25n^2 \) as:
\[
(9m)^2 - (5n)^2
\]
Using the difference of squares formula, this factors as:
\[
(9m - 5n)(9m + 5n)
\]
Since \( 9m + 5n \) is given as one of the factors, the other factor must be \( 9m - 5n \).

So, the other factor is \( 9m - 5n \).

Would you like a more detailed explanation? 

Here are five related questions:
1. How do you apply the difference of squares formula to factor expressions?
2. What are some other examples of quadratic expressions that can be factored using the difference of squares method?
3. Can the difference of squares formula be extended to complex numbers?
4. How would you solve an equation if one of its factors is a binomial like \( 9m + 5n \)?
5. How does factoring help in solving polynomial equations?

**Tip:** When factoring a quadratic expression, always check if it fits a known pattern, like difference of squares, perfect square trinomials, or simple quadratics. This can save time!

If one of the factors of 81m^2 - 25n^2 is 9m + 5n, which among the following is the other factor?

Learn how to factor the expression 81m^2 - 25n^2 using the difference of squares method. This problem explains step-by-step how to factor it, given that one of the factors is 9m + 5n. Suitable for students in Grades 8-10.

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