Initial program 0.1
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
Taylor expanded around -inf 0.1
\[\leadsto \left(\frac{\color{blue}{m - {m}^{2}}}{v} - 1\right) \cdot \left(1 - m\right)\]
Simplified0.1
\[\leadsto \left(\frac{\color{blue}{m - m \cdot m}}{v} - 1\right) \cdot \left(1 - m\right)\]
- Using strategy
rm Applied pow10.1
\[\leadsto \left(\frac{m - m \cdot m}{v} - 1\right) \cdot \color{blue}{{\left(1 - m\right)}^{1}}\]
Applied pow10.1
\[\leadsto \color{blue}{{\left(\frac{m - m \cdot m}{v} - 1\right)}^{1}} \cdot {\left(1 - m\right)}^{1}\]
Applied pow-prod-down0.1
\[\leadsto \color{blue}{{\left(\left(\frac{m - m \cdot m}{v} - 1\right) \cdot \left(1 - m\right)\right)}^{1}}\]
Simplified0.1
\[\leadsto {\color{blue}{\left(\frac{m}{v} \cdot \left(\left(1 - m\right) \cdot \left(1 - m\right)\right) - \left(1 - m\right)\right)}}^{1}\]
- Using strategy
rm Applied sub-neg0.1
\[\leadsto {\left(\frac{m}{v} \cdot \left(\left(1 - m\right) \cdot \color{blue}{\left(1 + \left(-m\right)\right)}\right) - \left(1 - m\right)\right)}^{1}\]
Applied distribute-rgt-in0.1
\[\leadsto {\left(\frac{m}{v} \cdot \color{blue}{\left(1 \cdot \left(1 - m\right) + \left(-m\right) \cdot \left(1 - m\right)\right)} - \left(1 - m\right)\right)}^{1}\]
Applied distribute-rgt-in0.1
\[\leadsto {\left(\color{blue}{\left(\left(1 \cdot \left(1 - m\right)\right) \cdot \frac{m}{v} + \left(\left(-m\right) \cdot \left(1 - m\right)\right) \cdot \frac{m}{v}\right)} - \left(1 - m\right)\right)}^{1}\]
Applied associate--l+0.1
\[\leadsto {\color{blue}{\left(\left(1 \cdot \left(1 - m\right)\right) \cdot \frac{m}{v} + \left(\left(\left(-m\right) \cdot \left(1 - m\right)\right) \cdot \frac{m}{v} - \left(1 - m\right)\right)\right)}}^{1}\]
Final simplification0.1
\[\leadsto \left(\left(-\left(\left(1 - m\right) \cdot m\right) \cdot \frac{m}{v}\right) - \left(1 - m\right)\right) + \left(1 - m\right) \cdot \frac{m}{v}\]
