2/5 (10x − 10y) −


3/4 (12x − 24y)

1 answer

To simplify the expression \( \frac{2}{5}(10x - 10y) - \frac{3}{4}(12x - 24y) \), follow these steps:

  1. Distribute the constants \( \frac{2}{5} \) and \( -\frac{3}{4} \) across the terms in the parentheses.

    \[ \frac{2}{5}(10x - 10y) = \frac{2}{5} \cdot 10x - \frac{2}{5} \cdot 10y = \frac{20}{5}x - \frac{20}{5}y = 4x - 4y \]

    \[ -\frac{3}{4}(12x - 24y) = -\frac{3}{4} \cdot 12x + \frac{3}{4} \cdot 24y = -\frac{36}{4}x + \frac{72}{4}y = -9x + 18y \]

  2. Now combine the results from both distributions:

    \[ 4x - 4y - 9x + 18y \]

  3. Combine like terms:

    \[ (4x - 9x) + (-4y + 18y) = -5x + 14y \]

Thus, the simplified expression is:

\[ -5x + 14y \]