Solve -a{left({left(-1/2ab^2right)}^{2}-2/3a^2b^4-5/2a^2{b}^{4}+5/12{a}^{2}{b}^4right)}^0-3ab{left(-frac{1}{2}aright)}^2+3a-frac{1}{4}{a}^3b

$$-a { \left( { \left(- \frac{ 1 }{ 2 } a { b }^{ 2 } \right) }^{ 2 } - \frac{ 2 }{ 3 } { a }^{ 2 } { b }^{ 4 } - \frac{ 5 }{ 2 } { a }^{ 2 } { b }^{ 4 } + \frac{ 5 }{ 12 } { a }^{ 2 } { b }^{ 4 } \right) }^{ 0 } -3ab { \left(- \frac{ 1 }{ 2 } a \right) }^{ 2 } +3a- \frac{ 1 }{ 4 } { a }^{ 3 } b$$

Factor

$$a\left(2-ba^{2}\right)$$

Solution Steps

Factor out -ba^{2}+3 in -3ab\left(-\frac{a}{2}\right)^{2}+3a-\frac{a^{3}b}{4}.

$$-a\left(\left(-\frac{1}{2}ab^{2}\right)^{2}-\frac{2}{3}a^{2}b^{4}-\frac{5}{2}a^{2}b^{4}+\frac{5}{12}a^{2}b^{4}\right)^{0}+\left(-ba^{2}+3\right)a$$

Factor out common term a by using distributive property.

$$a\left(-\left(\left(-\frac{1}{2}ab^{2}\right)^{2}-\frac{2}{3}a^{2}b^{4}-\frac{5}{2}a^{2}b^{4}+\frac{5}{12}a^{2}b^{4}\right)^{0}-ba^{2}+3\right)$$

Consider -\left(\left(-\frac{1}{2}ab^{2}\right)^{2}-\frac{2}{3}a^{2}b^{4}-\frac{5}{2}a^{2}b^{4}+\frac{5}{12}a^{2}b^{4}\right)^{0}-ba^{2}+3. Simplify.

$$-ba^{2}+2$$

Rewrite the complete factored expression.

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

Evaluate

$$a\left(2-ba^{2}\right)$$