Solve 7m^{2}+3mn+6n^{2}+(-5n^{3}+5mn+6m^2-n^2+6m^3+4mn-2n^2+m-2

$$7 m ^ { 2 } + 3 m n + 6 n ^ { 2 } + ( - 5 n ^ { 3 } + 5 m n + 6 m ^ { 2 } - n ^ { 2 } + 6 m ^ { 3 } + 4 m n - 2 n ^ { 2 } + m - 2$$

Evaluate

$$6m^{3}+13m^{2}+12mn+m-5n^{3}+3n^{2}-2$$

Solution Steps

Combine 3mn and 5mn to get 8mn.

$$7m^{2}+8mn+6n^{2}-5n^{3}+6m^{2}-n^{2}+6m^{3}+4mn-2n^{2}+m-2$$

Combine 7m^{2} and 6m^{2} to get 13m^{2}.

$$13m^{2}+8mn+6n^{2}-5n^{3}-n^{2}+6m^{3}+4mn-2n^{2}+m-2$$

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

$$13m^{2}+8mn+5n^{2}-5n^{3}+6m^{3}+4mn-2n^{2}+m-2$$

Combine 8mn and 4mn to get 12mn.

$$13m^{2}+12mn+5n^{2}-5n^{3}+6m^{3}-2n^{2}+m-2$$

Combine 5n^{2} and -2n^{2} to get 3n^{2}.

$$13m^{2}+12mn+3n^{2}-5n^{3}+6m^{3}+m-2$$

Differentiate w.r.t. m

$$18m^{2}+26m+12n+1$$