Simplify the expression completely.

Question

3(x−8y)−2(5x−4y)


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(7 points)

Answer 1

To simplify the expression \(3(x - 8y) - 2(5x - 4y)\), we will follow these steps:

1. Distribute the constants (3 and -2) across the terms inside the parentheses.
2. Combine like terms.

Let's begin by distributing:

1. Distributing 3 to \(x - 8y\): \[ 3(x - 8y) = 3x - 24y \]

2. Distributing -2 to \(5x - 4y\): \[ -2(5x - 4y) = -10x + 8y \]

Now, substituting the distributed terms back into the expression:

\[ 3(x - 8y) - 2(5x - 4y) = (3x - 24y) + (-10x + 8y) \]

Next, we combine like terms. The terms involving \(x\) are \(3x\) and \(-10x\), and the terms involving \(y\) are \(-24y\) and \(8y\).

3. Combining \(x\) terms: \[ 3x - 10x = -7x \]

4. Combining \(y\) terms: \[ -24y + 8y = -16y \]

Putting it all together, we get:

\[ -7x - 16y \]

Thus, the completely simplified expression is:

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