Solve (4a^{2}+b^2+a-5c+7)+(c^2-5+a-3b^2-6a^2)

$$( 4 a ^ { 2 } + b ^ { 2 } + a - 5 c + 7 ) + ( c ^ { 2 } - 5 + a - 3 b ^ { 2 } - 6 a ^ { 2 } )$$

Evaluate

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

Solution Steps

Subtract 5 from 7 to get 2.

$$4a^{2}+b^{2}+a-5c+2+c^{2}+a-3b^{2}-6a^{2}$$

Combine a and a to get 2a.

$$4a^{2}+b^{2}+2a-5c+2+c^{2}-3b^{2}-6a^{2}$$

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

$$4a^{2}-2b^{2}+2a-5c+2+c^{2}-6a^{2}$$

Combine 4a^{2} and -6a^{2} to get -2a^{2}.

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

Differentiate w.r.t. a

$$2-4a$$