Question

Simplify the expression completely.
3 (х - 8у) - 2(5х - 4y)
NOTE: You must show all work to receive credit for this question.

Answer 1

Let's simplify the expression \( 3 (x - 8y) - 2(5x - 4y) \) step by step.

1. **Distribute the constants**:

For the first term, \( 3(x - 8y) \):
\[
3(x - 8y) = 3x - 3 \cdot 8y = 3x - 24y
\]

For the second term, \( -2(5x - 4y) \):
\[
-2(5x - 4y) = -2 \cdot 5x + -2 \cdot (-4y) = -10x + 8y
\]

Now, we can rewrite the expression:
\[
3(x - 8y) - 2(5x - 4y) = (3x - 24y) + (-10x + 8y)
\]

2. **Combine like terms**:

Combine the \(x\) terms and the \(y\) terms:
- For the \(x\) terms: \( 3x - 10x = -7x \)
- For the \(y\) terms: \( -24y + 8y = -16y \)

Thus, the simplified expression is:
\[
-7x - 16y
\]

3. **Final result**:

The expression \( 3 (x - 8y) - 2(5x - 4y) \) simplifies completely to:
\[
\boxed{-7x - 16y}
\]