Find an expression which represents the difference (2x−3y) is(−7x−5y) in simplest terms.

The problem asks for an expression that represents the difference between \( (2x - 3y) \) and \( (-7x - 5y) \).

The difference of two expressions is found by subtracting the second expression from the first:

\[
(2x - 3y) - (-7x - 5y)
\]

Now, distribute the negative sign through the second expression:

\[
2x - 3y + 7x + 5y
\]

Next, combine the like terms:

- Combine the \( x \)-terms: \( 2x + 7x = 9x \)
- Combine the \( y \)-terms: \( -3y + 5y = 2y \)

So, the simplified expression is:

\[
9x + 2y
\]

Would you like further details or have any other questions?

Here are 5 related questions to explore this further:
1. How do you simplify the sum of two algebraic expressions?
2. What is the distributive property, and how does it apply in this problem?
3. What happens when you subtract a negative number from an expression?
4. How would the process change if there were three variables instead of two?
5. Can you explain why combining like terms is important in algebra?

**Tip:** When subtracting algebraic expressions, remember to distribute the negative sign across the entire second expression.

Find an expression which represents the difference (2x−3y) and (−7x−5y) in simplest terms.

Learn how to find the simplest expression for the difference between (2x - 3y) and (-7x - 5y). This problem covers key algebraic concepts like simplifying expressions and combining like terms, suitable for students in Grades 6-8.

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