-(x+2y)-4(x+2y) ²

To simplify the expression \(- (x + 2y) - 4(x + 2y)^2\), we will first work through each component step by step.

1. First, identify \((x + 2y)\) and \((x + 2y)^2\): \[ (x + 2y)^2 = (x + 2y)(x + 2y) = x^2 + 4xy + 4y^2 \]

2. Now substitute \((x + 2y)^2\) in the expression: \[ - (x + 2y) - 4(x + 2y)^2 = - (x + 2y) - 4(x^2 + 4xy + 4y^2) \]

3. Distribute the \(-4\) through the squared term: \[ - (x + 2y) - (4x^2 + 16xy + 16y^2) \]

4. Now, combine the terms: \[ -x - 2y - 4x^2 - 16xy - 16y^2 \]

Thus, the simplified expression is: \[ -4x^2 - 16xy - 16y^2 - x - 2y \]

You can also rearrange it if desired, but this is the simplified version.