To simplify the given expression:

$-2(4x + 5y) - 4(8x - 7y)$

Step-by-Step Solution:

1. Distribute $-2$ to $(4x + 5y)$: $-2 \cdot 4x = -8x, \quad -2 \cdot 5y = -10y$ Result: $-8x - 10y$

2. Distribute $-4$ to $(8x - 7y)$: $-4 \cdot 8x = -32x, \quad -4 \cdot -7y = +28y$ Result: $-32x + 28y$

3. Combine the results: $(-8x - 10y) + (-32x + 28y)$

4. Group like terms: $(-8x - 32x) + (-10y + 28y)$

5. Simplify: $-8x - 32x = -40x, \quad -10y + 28y = 18y$

6. Final expression: $-40x + 18y$

Simplified Expression:

$\boxed{-40x + 18y}$

Let me know if you want details or have questions!

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Related Questions:

1. How do you apply the distributive property in algebraic expressions?
2. Can you simplify another expression with more variables?
3. How would this process change with fractional coefficients?
4. What is the significance of combining like terms?
5. How do negative signs impact the distributive property?

Tip:

Always double-check your sign changes when distributing negative coefficients to avoid errors.