Solve (2a^{2}-3b^{2}+4c^{2})+(b^{2}-a^{2}+c^2)+(c^2+a^2-b^2)

$$( 2 a ^ { 2 } - 3 b ^ { 2 } + 4 c ^ { 2 } ) + ( b ^ { 2 } - a ^ { 2 } + c ^ { 2 } ) + ( c ^ { 2 } + a ^ { 2 } - b ^ { 2 } )$$

Evaluate

$$2a^{2}-3b^{2}+6c^{2}$$

Solution Steps

Combine -3b^{2} and b^{2} to get -2b^{2}.

$$2a^{2}-2b^{2}+4c^{2}-a^{2}+c^{2}+c^{2}+a^{2}-b^{2}$$

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

$$a^{2}-2b^{2}+4c^{2}+c^{2}+c^{2}+a^{2}-b^{2}$$

Combine 4c^{2} and c^{2} to get 5c^{2}.

$$a^{2}-2b^{2}+5c^{2}+c^{2}+a^{2}-b^{2}$$

Combine 5c^{2} and c^{2} to get 6c^{2}.

$$a^{2}-2b^{2}+6c^{2}+a^{2}-b^{2}$$

Combine a^{2} and a^{2} to get 2a^{2}.

$$2a^{2}-2b^{2}+6c^{2}-b^{2}$$

Combine -2b^{2} and -b^{2} to get -3b^{2}.

$$2a^{2}-3b^{2}+6c^{2}$$

Differentiate w.r.t. a

$$4a$$