Solve 3mn+6m^2-n^2+3-m^2-3mn+2n^2-4

$$3 m n + 6 m ^ { 2 } - n ^ { 2 } + 3 - m ^ { 2 } - 3 m n + 2 n ^ { 2 } - 4$$

Evaluate

$$5m^{2}+n^{2}-1$$

Solution Steps

Combine 6m^{2} and -m^{2} to get 5m^{2}.

$$3mn+5m^{2}-n^{2}+3-3mn+2n^{2}-4$$

Combine 3mn and -3mn to get 0.

$$5m^{2}-n^{2}+3+2n^{2}-4$$

Combine -n^{2} and 2n^{2} to get n^{2}.

$$5m^{2}+n^{2}+3-4$$

Subtract 4 from 3 to get -1.

$$5m^{2}+n^{2}-1$$

Differentiate w.r.t. n

$$2n$$