Question

Simplify the expression completely.

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:

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