Initial program 6.0
\[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\]
- Using strategy
rm Applied associate-*l*6.0
\[\leadsto x \cdot x - \color{blue}{y \cdot \left(4 \cdot \left(z \cdot z - t\right)\right)}\]
- Using strategy
rm Applied add-cube-cbrt6.8
\[\leadsto x \cdot x - \color{blue}{\left(\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}\right)} \cdot \left(4 \cdot \left(z \cdot z - t\right)\right)\]
Applied associate-*l*6.8
\[\leadsto x \cdot x - \color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \left(\sqrt[3]{y} \cdot \left(4 \cdot \left(z \cdot z - t\right)\right)\right)}\]
- Using strategy
rm Applied sub-neg6.8
\[\leadsto x \cdot x - \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \left(\sqrt[3]{y} \cdot \left(4 \cdot \color{blue}{\left(z \cdot z + \left(-t\right)\right)}\right)\right)\]
Applied distribute-lft-in6.8
\[\leadsto x \cdot x - \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \left(\sqrt[3]{y} \cdot \color{blue}{\left(4 \cdot \left(z \cdot z\right) + 4 \cdot \left(-t\right)\right)}\right)\]
Applied distribute-lft-in6.8
\[\leadsto x \cdot x - \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \color{blue}{\left(\sqrt[3]{y} \cdot \left(4 \cdot \left(z \cdot z\right)\right) + \sqrt[3]{y} \cdot \left(4 \cdot \left(-t\right)\right)\right)}\]
Applied distribute-lft-in6.8
\[\leadsto x \cdot x - \color{blue}{\left(\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \left(\sqrt[3]{y} \cdot \left(4 \cdot \left(z \cdot z\right)\right)\right) + \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \left(\sqrt[3]{y} \cdot \left(4 \cdot \left(-t\right)\right)\right)\right)}\]
Simplified0.7
\[\leadsto x \cdot x - \left(\color{blue}{\left(y \cdot z\right) \cdot \left(4 \cdot z\right)} + \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \left(\sqrt[3]{y} \cdot \left(4 \cdot \left(-t\right)\right)\right)\right)\]
Simplified0.1
\[\leadsto x \cdot x - \left(\left(y \cdot z\right) \cdot \left(4 \cdot z\right) + \color{blue}{\left(-y\right) \cdot \left(t \cdot 4\right)}\right)\]
Final simplification0.1
\[\leadsto x \cdot x - \left(\left(y \cdot z\right) \cdot \left(4 \cdot z\right) + \left(-y\right) \cdot \left(t \cdot 4\right)\right)\]
