Solve (3m^2-5n^2+2m+6n-3)+(4-4n^2+5m-12n+2m^2)

$$( 3 m ^ { 2 } - 5 n ^ { 2 } + 2 m + 6 n - 3 ) + ( 4 - 4 n ^ { 2 } + 5 m - 12 n + 2 m ^ { 2 } )$$

Evaluate

$$5m^{2}+7m-9n^{2}-6n+1$$

Solution Steps

Add -3 and 4 to get 1.

$$3m^{2}-5n^{2}+2m+6n+1-4n^{2}+5m-12n+2m^{2}$$

Combine -5n^{2} and -4n^{2} to get -9n^{2}.

$$3m^{2}-9n^{2}+2m+6n+1+5m-12n+2m^{2}$$

Combine 2m and 5m to get 7m.

$$3m^{2}-9n^{2}+7m+6n+1-12n+2m^{2}$$

Combine 6n and -12n to get -6n.

$$3m^{2}-9n^{2}+7m-6n+1+2m^{2}$$

Combine 3m^{2} and 2m^{2} to get 5m^{2}.

$$5m^{2}-9n^{2}+7m-6n+1$$

Differentiate w.r.t. m

$$10m+7$$