Solve 1/12a(4a-3a^{2}-18a^{2}b)+1/6b^{2}-2/3|(-1/2b)^2-3ab+frac{1}{2}a^2|-(-frac{1}{2}a)^3+(frac{3}{2}ab+frac{1}{8}a)(-a)^2

$$\frac { 1 } { 12 } a ( 4 a - 3 a ^ { 2 } - 18 a ^ { 2 } b ) + \frac { 1 } { 6 } b ^ { 2 } - \frac { 2 } { 3 } | ( - \frac { 1 } { 2 } b ) ^ { 2 } - 3 a b + \frac { 1 } { 2 } a ^ { 2 } | - ( - \frac { 1 } { 2 } a ) ^ { 3 } + ( \frac { 3 } { 2 } a b + \frac { 1 } { 8 } a ) ( - a ) ^ { 2 }$$

Factor

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

Solution Steps

Factor out \frac{1}{24}.

$$\frac{2a\left(4a-3a^{2}-18a^{2}b\right)+4b^{2}-16|\left(-\frac{b}{2}\right)^{2}-3ab+\frac{a^{2}}{2}|+3a^{3}+3\left(12ab+a\right)a^{2}}{24}$$

Evaluate

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