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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 -ba^{2}+3 in -3ab\left(-\frac{a}{2}\right)^{2}+3a-\frac{a^{3}b}{4}.
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)
Factor out common term a by using distributive property.
-ba^{2}+4
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.
a\left(-ba^{2}+4\right)
Rewrite the complete factored expression.