Simplify the expression.

Question

−8(x−3y)+5(−2x−7y)

NOTE: On the sample work, this is a multiple choice question, but on the test, you will be required to show your work for each step to receive credit for this question. Practice writing this out on paper now, so you are prepared to show your work for the test.

(1 point)
Responses

18x+59y
18 x plus 59 y

−18x−11y
negative 18 x minus 11 y

2x+11y
2 x plus 11 y

−2x−11y

Answer 1

To simplify the expression \(-8(x - 3y) + 5(-2x - 7y)\), we can follow the steps below:

1. Distribute \(-8\) in the first term: \[ -8(x - 3y) = -8 \cdot x + (-8) \cdot (-3y) = -8x + 24y \]

2. Distribute \(5\) in the second term: \[ 5(-2x - 7y) = 5 \cdot (-2x) + 5 \cdot (-7y) = -10x - 35y \]

3. Combine the two results: \[ -8x + 24y - 10x - 35y \]

4. Combine like terms for \(x\) values: \[ -8x - 10x = -18x \]

5. Combine like terms for \(y\) values: \[ 24y - 35y = -11y \]

6. Put the results together: \[ -18x - 11y \]

So, the simplified expression is: \[ \boxed{-18x - 11y} \]