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To solve this, we need to carefully subtract the two expressions as specified in the problem.

The problem asks for the difference when \((7x + 9y)\) is subtracted **from** \((x + 5y)\). This means we write it as:

\[
(x + 5y) - (7x + 9y)
\]

Now, let's distribute the negative sign across the second set of parentheses:

\[
x + 5y - 7x - 9y
\]

Next, we combine like terms:

- For the \(x\)-terms: \(x - 7x = -6x\)
- For the \(y\)-terms: \(5y - 9y = -4y\)

So, the simplified expression is:

\[
-6x - 4y
\]

This is the simplest form of the expression. Let me know if you'd like further clarification!

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Would you like details on any of these steps?

Here are 5 related questions you might find useful:
1. How do you subtract polynomials in general?
2. What are like terms, and how do we combine them?
3. How do you distribute negative signs in algebra?
4. Can this problem be extended to three variables instead of two?
5. How do we check if an algebraic expression is fully simplified?

**Tip:** Always be careful with subtraction; the order of the terms matters!

Find an expression which represents the difference when (7x + 9y) is subtracted from (x + 5y) in simplest terms.

Learn how to simplify expressions involving polynomial subtraction, specifically the difference between (x + 5y) and (7x + 9y). This step-by-step explanation covers combining like terms and understanding the effect of negative signs. Suitable for students in Grades 6-8.

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