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

−2x−11y
negative 2 x minus 11 y

18x+59y
18 x plus 59 y

−18x−11y
negative 18 x minus 11 y

2x+11y

Answer 1

To simplify the expression \(-8(x−3y)+5(−2x−7y)\), we'll follow these steps:

1. Distribute the coefficients:

   • Distributing \(-8\) in the first term: \[ -8(x) + -8(-3y) = -8x + 24y \]

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

2. Combine the results: Now we combine the results from both distributions: \[ (-8x + 24y) + (-10x - 35y) \]

   • Combine like terms for \(x\): \[ -8x - 10x = -18x \]
   • Combine like terms for \(y\): \[ 24y - 35y = -11y \]

3. Write the final expression: Combining both parts gives us: \[ -18x - 11y \]

So, the simplified expression is \(-18x - 11y\).

The correct choice from the options given is: −18x−11y (negative 18 x minus 11 y)