Solve (1/4a^{2}-1/2b^{2}+1/6ab)+|-(ab-1/2b^2+a^2)-(frac{2}{3}ab-b^2-frac{3}{4}a^2)|

$$( \frac { 1 } { 4 } a ^ { 2 } - \frac { 1 } { 2 } b ^ { 2 } + \frac { 1 } { 6 } a b ) + | - ( a b - \frac { 1 } { 2 } b ^ { 2 } + a ^ { 2 } ) - ( \frac { 2 } { 3 } a b - b ^ { 2 } - \frac { 3 } { 4 } a ^ { 2 } ) |$$

Factor

$$\frac{12|-\frac{5ab}{3}+\frac{3b^{2}}{2}-\frac{a^{2}}{4}|+2ab+3a^{2}-6b^{2}}{12}$$

Solution Steps

Factor out \frac{1}{12}.

$$\frac{3a^{2}-6b^{2}+2ab+12|-\left(ab-\frac{b^{2}}{2}+a^{2}\right)-\left(\frac{2ab}{3}-b^{2}-\frac{3a^{2}}{4}\right)|}{12}$$

Evaluate

$$\frac{ab}{6}+|-\frac{5ab}{3}+\frac{3b^{2}}{2}-\frac{a^{2}}{4}|+\frac{a^{2}}{4}-\frac{b^{2}}{2}$$