Consider the following expression.
-2m(m + n - 4)+ 5(- 2m + 2n) + n(m + 4m - 5)
Which of the following is an equivalent expression?
-10m^2 + 4n^2 - mn - 2m + 5n
-10m^2 + 4n^2 - 3mn - 2m + 5n
-2m^2 + 4n^2 - mn - 2m + 5n
-2m^2 + 4n^2 - 3mn - 2m + 5n
Expanding and simplifying the given expression:
-2m(m + n - 4) + 5(-2m + 2n) + n(m + 4m - 5)
= -2m^2 - 2mn + 8m + 5(-2m + 2n) + n(5m - 5)
= -2m^2 - 2mn + 8m - 10m + 10n + 5mn - 5n
= -2m^2 + 4n^2 - 3mn + 5m + 5n
Therefore, the equivalent expression is -2m^2 + 4n^2 - 3mn + 5m + 5n.
The answer is -10m^2 + 4n^2 - 3mn - 2m + 5n.