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

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

Evaluate

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

Solution Steps

To find the opposite of -5b^{2}+6c^{2}-a^{2}, find the opposite of each term.

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

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

$$3a^{2}+b^{2}+7c^{2}-6c^{2}+a^{2}$$

Combine 7c^{2} and -6c^{2} to get c^{2}.

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

Combine 3a^{2} and a^{2} to get 4a^{2}.

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

Expand

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

Solution Steps

To find the opposite of -5b^{2}+6c^{2}-a^{2}, find the opposite of each term.

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

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

$$3a^{2}+b^{2}+7c^{2}-6c^{2}+a^{2}$$

Combine 7c^{2} and -6c^{2} to get c^{2}.

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

Combine 3a^{2} and a^{2} to get 4a^{2}.

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