Solve (5)a^{2}-(3a^2-b^2)-3(a^2-2b^2)

$$( 5 ) a ^ { 2 } - ( 3 a ^ { 2 } - b ^ { 2 } ) - 3 ( a ^ { 2 } - 2 b ^ { 2 } )$$

Evaluate

$$7b^{2}-a^{2}$$

Solution Steps

To find the opposite of 3a^{2}-b^{2}, find the opposite of each term.

$$5a^{2}-3a^{2}+b^{2}-3\left(a^{2}-2b^{2}\right)$$

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

$$2a^{2}+b^{2}-3\left(a^{2}-2b^{2}\right)$$

Use the distributive property to multiply -3 by a^{2}-2b^{2}.

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

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

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

Combine b^{2} and 6b^{2} to get 7b^{2}.

$$-a^{2}+7b^{2}$$

Expand

$$7b^{2}-a^{2}$$

Solution Steps

To find the opposite of 3a^{2}-b^{2}, find the opposite of each term.

$$5a^{2}-3a^{2}+b^{2}-3\left(a^{2}-2b^{2}\right)$$

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

$$2a^{2}+b^{2}-3\left(a^{2}-2b^{2}\right)$$

Use the distributive property to multiply -3 by a^{2}-2b^{2}.

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

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

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

Combine b^{2} and 6b^{2} to get 7b^{2}.

$$-a^{2}+7b^{2}$$