Solve: (-4-y)(-2x-?) = 8x-16-4y+2xy - Finding the Missing Term

Complete the missing element

$(-4-y)(-2x-?)=8x-16-4y+2xy$

To solve for the missing element, we'll employ the distributive property as follows:

1. Let's expand $(-4-y)(-2x-?)$:

• Multiply $-4$ by $-2x$: $-4 \times -2x = 8x$.
• Multiply $-4$ by the unknown: $-4 \times ? = -4?$.
• Multiply $-y$ by $-2x$: $-y \times -2x = 2xy$.
• Multiply $-y$ by the unknown: $-y \times ? = -y?$.

2. Combine these results to form the expression:

3. Compare this expression with the target expression $8x - 16 - 4y + 2xy$:

• We already have $8x$ and $2xy$ matching, so we're left to make the terms $-4?$ and $-y?$ match $-16$ and $-4y$ respectively.

4. From $-4? = -16$, we solve for $?$:

Thus, the missing number $-4$ is needed to get the resulting expression to match.

Therefore, the missing element is $\boxed{-4}$.