https://file.aiquickdraw.com/mathbot/file/1727083143072qgql3kq3.jpg

The expression in the image is:

\[
x - 3y(x - 5y) - (-6xy + 7x)
\]

Let’s simplify this step-by-step:

1. **Distribute the -3y in the second term**:
   \[
   - 3y(x - 5y) = -3yx + 15y^2
   \]

   So the expression becomes:
   \[
   x - 3yx + 15y^2 - (-6xy + 7x)
   \]

2. **Simplify the subtraction of the third term**:
   \[
   - (-6xy + 7x) = 6xy - 7x
   \]

   Now, we have:
   \[
   x - 3yx + 15y^2 + 6xy - 7x
   \]

3. **Combine like terms**:
   - Combine the \(x\) terms: \(x - 7x = -6x\)
   - Combine the \(xy\) terms: \(-3yx + 6xy = 3xy\)
   
   So the final simplified expression is:
   \[
   -6x + 3xy + 15y^2
   \]

This is the simplified form of the expression.

Would you like any further details on this, or have any questions? Here are five follow-up questions you could consider:

1. How would the result change if one of the variables, say \(y\), was set to zero?
2. What would the expression look like if we factored it?
3. How would the result change if we expanded a different part of the expression first?
4. Can this expression represent a geometric shape in the \(xy\)-plane?
5. What would happen if we added an extra term like \(+2xy^2\)?

**Tip**: Always check if terms can be combined or factored when simplifying expressions!

Learn how to simplify the algebraic expression x - 3y(x - 5y) - (-6xy + 7x) using the distributive property and combining like terms. This step-by-step solution is suitable for students in Grades 9-11.

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