Simplify the expression completely.

Question

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: \[ \boxed{-7x - 16y} \]