Question
Simplify the expression completely.
3(x−8y)−2(5x−4y)
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3(x−8y)−2(5x−4y)
NOTE: You must show all work to receive credit for this question. You can use the math keyboard to type out your solution or upload an image of your handwritten work.
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Answered by
GPT-4o mini
To simplify the expression \(3(x - 8y) - 2(5x - 4y)\), follow these steps:
1. **Distribute** the constants 3 and -2 across the terms inside the parentheses:
\[
3(x - 8y) = 3x - 24y
\]
\[
-2(5x - 4y) = -10x + 8y
\]
2. **Substitute** these results back into the expression:
\[
3(x - 8y) - 2(5x - 4y) = (3x - 24y) + (-10x + 8y)
\]
3. **Combine** like terms (combine the \(x\) terms and the \(y\) terms):
- Combine the \(x\) terms: \(3x - 10x = -7x\)
- Combine the \(y\) terms: \(-24y + 8y = -16y\)
4. **Write the final simplified expression**:
\[
-7x - 16y
\]
Thus, the completely simplified expression is:
\[
\boxed{-7x - 16y}
\]
1. **Distribute** the constants 3 and -2 across the terms inside the parentheses:
\[
3(x - 8y) = 3x - 24y
\]
\[
-2(5x - 4y) = -10x + 8y
\]
2. **Substitute** these results back into the expression:
\[
3(x - 8y) - 2(5x - 4y) = (3x - 24y) + (-10x + 8y)
\]
3. **Combine** like terms (combine the \(x\) terms and the \(y\) terms):
- Combine the \(x\) terms: \(3x - 10x = -7x\)
- Combine the \(y\) terms: \(-24y + 8y = -16y\)
4. **Write the final simplified expression**:
\[
-7x - 16y
\]
Thus, the completely simplified expression is:
\[
\boxed{-7x - 16y}
\]
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