Solve a^2+b^2-(1/2a^2+6b)

$$a ^ { 2 } + b ^ { 2 } - ( \frac { 1 } { 2 } a ^ { 2 } + 6 b )$$

Evaluate

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

Solution Steps

To find the opposite of \frac{1}{2}a^{2}+6b, find the opposite of each term.

$$a^{2}+b^{2}-\frac{1}{2}a^{2}-6b$$

Combine a^{2} and -\frac{1}{2}a^{2} to get \frac{1}{2}a^{2}.

$$\frac{1}{2}a^{2}+b^{2}-6b$$

Expand

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

Solution Steps

To find the opposite of \frac{1}{2}a^{2}+6b, find the opposite of each term.

$$a^{2}+b^{2}-\frac{1}{2}a^{2}-6b$$

Combine a^{2} and -\frac{1}{2}a^{2} to get \frac{1}{2}a^{2}.

$$\frac{1}{2}a^{2}+b^{2}-6b$$