Solve a[(-1/2ab^{2})^{2}-(2/3a^{2}b^{4}-5/2a^{2}b^{4})+5/12a^{2}b^4]^0-3ab*(-frac{1}{2}a)^2+3a-frac{1}{4}a^3b

$$a [ ( - \frac { 1 } { 2 } a b ^ { 2 } ) ^ { 2 } - ( \frac { 2 } { 3 } a ^ { 2 } b ^ { 4 } - \frac { 5 } { 2 } a ^ { 2 } b ^ { 4 } ) + \frac { 5 } { 12 } a ^ { 2 } b ^ { 4 } ] ^ { 0 } - 3 a b \cdot ( - \frac { 1 } { 2 } a ) ^ { 2 } + 3 a - \frac { 1 } { 4 } a ^ { 3 } b$$

Factor

$$a\left(4-ba^{2}\right)$$

Solution Steps

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

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

Factor out common term a by using distributive property.

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

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

$$-ba^{2}+4$$

Rewrite the complete factored expression.

$$a\left(-ba^{2}+4\right)$$

Evaluate

$$a\left(4-ba^{2}\right)$$