Rewrite in simplest terms: 4, left parenthesis, 5, y, plus, 2, z, right parenthesis, plus, 8, z, minus, 4, left parenthesis, 5, z, minus, 2, y, right parenthesis4(5y+2z)+8z−4(5z−2y)

Answer 1

To simplify the expression \(4(5y + 2z) + 8z - 4(5z - 2y)\), we can follow these steps:

1. Distribute the 4 in the first term: \[ 4(5y) + 4(2z) = 20y + 8z \]

2. Distribute the -4 in the second term: \[ -4(5z) + -4(-2y) = -20z + 8y \]

3. Now, combine all the terms together: \[ 20y + 8z + 8z - 20z + 8y \]

4. Combine like terms:

   • For \(y\): \(20y + 8y = 28y\)
   • For \(z\): \(8z + 8z - 20z = -4z\)

5. The simplified expression is: \[ 28y - 4z \]

So, the final answer is: \[ 28y - 4z \]