To solve the expression \((5x - 10)(3x + 15)\), we'll use the distributive property (also known as the FOIL method for binomials):

\[
(5x - 10)(3x + 15)
\]

Expanding each term:

1. **First**: \(5x \times 3x = 15x^2\)
2. **Outer**: \(5x \times 15 = 75x\)
3. **Inner**: \(-10 \times 3x = -30x\)
4. **Last**: \(-10 \times 15 = -150\)

Now, combine all these terms together:

\[
15x^2 + 75x - 30x - 150
\]

Combine like terms:

\[
15x^2 + 45x - 150
\]

So, the expanded form of \((5x - 10)(3x + 15)\) is:

\[
15x^2 + 45x - 150
\]

Would you like more details, or do you have any questions about this solution? Here are five related questions you might find helpful:

1. How do you factor out a common factor from the polynomial \(15x^2 + 45x - 150\)?
2. What is the significance of the distributive property in algebra?
3. How would you solve the equation if it was set equal to zero, like \((5x - 10)(3x + 15) = 0\)?
4. Can you expand and simplify \((2x + 3)(4x - 5)\)?
5. How do you solve quadratic equations after expanding binomials?

**Tip:** When expanding binomials, always ensure you combine like terms to simplify the expression fully.

Learn how to expand and simplify the polynomial expression (5x – 10)(3x + 15) using the distributive property (FOIL method). This problem covers key algebraic concepts, suitable for students in Grades 8-10.

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