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-ba^{3}
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-ba^{3}
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\frac{\frac{1}{4}\times 2ba^{2}\left(ba^{2}+2\right)}{-\frac{3}{2}ab}+\frac{2}{3}a\left(1-a^{2}b\right)
Factor the expressions that are not already factored in \frac{\left(\frac{1}{2}a^{2}b+1\right)^{2}+\left(\frac{1}{2}a^{2}b+1\right)\left(\frac{1}{2}a^{2}b-1\right)}{-\frac{3}{2}ab}.
\frac{\frac{1}{4}\times 2a\left(ba^{2}+2\right)}{-\frac{3}{2}}+\frac{2}{3}a\left(1-a^{2}b\right)
Cancel out ab in both numerator and denominator.
\frac{\frac{1}{2}a\left(ba^{2}+2\right)}{-\frac{3}{2}}+\frac{2}{3}a\left(1-a^{2}b\right)
Multiply \frac{1}{4} and 2 to get \frac{1}{2}.
-\frac{1}{3}a\left(ba^{2}+2\right)+\frac{2}{3}a\left(1-a^{2}b\right)
Divide \frac{1}{2}a\left(ba^{2}+2\right) by -\frac{3}{2} to get -\frac{1}{3}a\left(ba^{2}+2\right).
-\frac{1}{3}ba^{3}-\frac{2}{3}a+\frac{2}{3}a\left(1-a^{2}b\right)
Use the distributive property to multiply -\frac{1}{3}a by ba^{2}+2.
-\frac{1}{3}ba^{3}-\frac{2}{3}a+\frac{2}{3}a-\frac{2}{3}a^{3}b
Use the distributive property to multiply \frac{2}{3}a by 1-a^{2}b.
-\frac{1}{3}ba^{3}-\frac{2}{3}a^{3}b
Combine -\frac{2}{3}a and \frac{2}{3}a to get 0.
-ba^{3}
Combine -\frac{1}{3}ba^{3} and -\frac{2}{3}a^{3}b to get -ba^{3}.
\frac{\frac{1}{4}\times 2ba^{2}\left(ba^{2}+2\right)}{-\frac{3}{2}ab}+\frac{2}{3}a\left(1-a^{2}b\right)
Factor the expressions that are not already factored in \frac{\left(\frac{1}{2}a^{2}b+1\right)^{2}+\left(\frac{1}{2}a^{2}b+1\right)\left(\frac{1}{2}a^{2}b-1\right)}{-\frac{3}{2}ab}.
\frac{\frac{1}{4}\times 2a\left(ba^{2}+2\right)}{-\frac{3}{2}}+\frac{2}{3}a\left(1-a^{2}b\right)
Cancel out ab in both numerator and denominator.
\frac{\frac{1}{2}a\left(ba^{2}+2\right)}{-\frac{3}{2}}+\frac{2}{3}a\left(1-a^{2}b\right)
Multiply \frac{1}{4} and 2 to get \frac{1}{2}.
-\frac{1}{3}a\left(ba^{2}+2\right)+\frac{2}{3}a\left(1-a^{2}b\right)
Divide \frac{1}{2}a\left(ba^{2}+2\right) by -\frac{3}{2} to get -\frac{1}{3}a\left(ba^{2}+2\right).
-\frac{1}{3}ba^{3}-\frac{2}{3}a+\frac{2}{3}a\left(1-a^{2}b\right)
Use the distributive property to multiply -\frac{1}{3}a by ba^{2}+2.
-\frac{1}{3}ba^{3}-\frac{2}{3}a+\frac{2}{3}a-\frac{2}{3}a^{3}b
Use the distributive property to multiply \frac{2}{3}a by 1-a^{2}b.
-\frac{1}{3}ba^{3}-\frac{2}{3}a^{3}b
Combine -\frac{2}{3}a and \frac{2}{3}a to get 0.
-ba^{3}
Combine -\frac{1}{3}ba^{3} and -\frac{2}{3}a^{3}b to get -ba^{3}.
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