We can simplify the expression \( 2(2x - 3y)(2x + 5y) \) by first focusing on multiplying the binomials and then applying the outer factor.

1. **Multiply the binomials**:
\[
(2x - 3y)(2x + 5y) = 4x^2 + 10xy - 6xy - 15y^2
\]
Combine like terms:
\[
= 4x^2 + 4xy - 15y^2
\]

2. **Now multiply the result by 2**:
\[
2(4x^2 + 4xy - 15y^2) = 8x^2 + 8xy - 30y^2
\]

Thus, the simplified expression is:
\[
8x^2 + 8xy - 30y^2
\]

Would you like more details on any step?

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Here are 5 related questions:
1. How would the expression change if the outer coefficient was different?
2. Can you solve a similar expression with different variables?
3. What happens if we replace \( y \) with a constant value?
4. How would the result change if one of the binomials had a negative term?
5. Can you expand a cubic expression using a similar process?

**Tip**: Always simplify inside the parentheses first before applying any external factors.

Explore the simplification of the expression 2(2x - 3y)(2x + 5y) with a detailed step-by-step approach. Learn key algebraic concepts such as polynomial expansion and the distributive property, ideal for students in Grades 8-10.

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