Which expression is equivalent to (9m^2 + 5mn - 4n^2)-(7m^2 + 3mn + 6n^2)?
A. 16m^4 + 8m^2n^2 + 2n^4
B. 16m^2+8mn+2n^2
C. 2m^2 + 8mn + 2n^2
D. 2m^2 +2mn - 10n^2
The expression (9m^2 + 5mn - 4n^2)-(7m^2 + 3mn + 6n^2) can be simplified by distributing the negative sign to each term inside the parentheses:
(9m^2 + 5mn - 4n^2) - (7m^2 + 3mn + 6n^2) = 9m^2 + 5mn - 4n^2 - 7m^2 - 3mn - 6n^2
Combining like terms:
= (9m^2 - 7m^2) + (5mn - 3mn) + (-4n^2 - 6n^2)
Simplifying further:
= 2m^2 + 2mn - 10n^2
Therefore, the equivalent expression is D. 2m^2 + 2mn - 10n^2.