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The expression given is:

\[
(-10x + 3y) \cdot (10x + 3y)
\]

This is a product of two binomials. We can use the distributive property (also known as the FOIL method for binomials) to expand this expression.

Let's break it down:

1. **First:** Multiply the first terms of each binomial:
   \[
   (-10x) \cdot (10x) = -100x^2
   \]

2. **Outer:** Multiply the outer terms:
   \[
   (-10x) \cdot (3y) = -30xy
   \]

3. **Inner:** Multiply the inner terms:
   \[
   (3y) \cdot (10x) = 30xy
   \]

4. **Last:** Multiply the last terms:
   \[
   (3y) \cdot (3y) = 9y^2
   \]

Now, sum all these terms together:
\[
-100x^2 - 30xy + 30xy + 9y^2
\]

The \(-30xy\) and \(30xy\) terms cancel each other out, so the final result is:

\[
-100x^2 + 9y^2
\]

Thus, the expanded form of the expression is:

\[
-100x^2 + 9y^2
\]

Would you like further details on any part of the process, or do you have any questions?

Here are five related questions you might explore:
1. What happens when you multiply two binomials with different terms?
2. How does the distributive property work for polynomials with more than two terms?
3. Can you expand \((x - y)(x + y)\) and compare it with the result from this problem?
4. How do you factor the expression \( -100x^2 + 9y^2 \)?
5. What is the geometric interpretation of squaring a binomial?

**Tip:** When multiplying binomials, always check if any terms cancel out after expanding, which simplifies the expression.

Expand and simplify the expression (-10x + 3y) · (10x + 3y) using the distributive property. Learn the step-by-step solution involving the multiplication of binomials and identification of the difference of squares, suitable for students in Grades 8-10.

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