Math Problem Solver

\[8.94 \cdot 8.94 \cdot 8.94 - \frac{3.56 \cdot 3.56 \cdot 3.56}{8.94} \cdot 8.94 + 8.94 \cdot 3.56 + 3.56 \cdot 3.56 = \frac{89237371}{125000} = 713.898968\]

\[\begin{aligned}8.94 \cdot 8.94 \cdot 8.94 - \frac{3.56 \cdot 3.56 \cdot 3.56}{8.94} \cdot 8.94 + 8.94 \cdot 3.56 + 3.56 \cdot 3.56& = \left(8 + \frac{94}{100}\right) \cdot \left(8 + \frac{94}{100}\right) \cdot \left(8 + \frac{94}{100}\right) - \left(3 + \frac{56}{100}\right) \cdot \left(3 + \frac{56}{100}\right) \cdot \left(3 + \frac{56}{100}\right) \cdot \frac{1}{8 + \frac{94}{100}} \cdot \left(8 + \frac{94}{100}\right) + \left(8 + \frac{94}{100}\right) \cdot \left(3 + \frac{56}{100}\right) + \left(3 + \frac{56}{100}\right) \cdot \left(3 + \frac{56}{100}\right)\\& = \left(8 + \frac{47}{50}\right) \cdot \left(8 + \frac{94}{100}\right) \cdot \left(8 + \frac{94}{100}\right) - \left(3 + \frac{56}{100}\right) \cdot \left(3 + \frac{56}{100}\right) \cdot \left(3 + \frac{56}{100}\right) \cdot \frac{1}{8 + \frac{94}{100}} \cdot \left(8 + \frac{94}{100}\right) + \left(8 + \frac{94}{100}\right) \cdot \left(3 + \frac{56}{100}\right) + \left(3 + \frac{56}{100}\right) \cdot \left(3 + \frac{56}{100}\right)\\& = \frac{447}{50} \cdot \left(8 + \frac{94}{100}\right) \cdot \left(8 + \frac{94}{100}\right) - \left(3 + \frac{56}{100}\right) \cdot \left(3 + \frac{56}{100}\right) \cdot \left(3 + \frac{56}{100}\right) \cdot \frac{1}{8 + \frac{94}{100}} \cdot \left(8 + \frac{94}{100}\right) + \left(8 + \frac{94}{100}\right) \cdot \left(3 + \frac{56}{100}\right) + \left(3 + \frac{56}{100}\right) \cdot \left(3 + \frac{56}{100}\right)\\& = \frac{447}{50} \cdot \left(8 + \frac{47}{50}\right) \cdot \left(8 + \frac{94}{100}\right) - \left(3 + \frac{56}{100}\right) \cdot \left(3 + \frac{56}{100}\right) \cdot \left(3 + \frac{56}{100}\right) \cdot \frac{1}{8 + \frac{94}{100}} \cdot \left(8 + \frac{94}{100}\right) + \left(8 + \frac{94}{100}\right) \cdot \left(3 + \frac{56}{100}\right) + \left(3 + \frac{56}{100}\right) \cdot \left(3 + \frac{56}{100}\right)\\& = \frac{447}{50} \cdot \frac{447}{50} \cdot \left(8 + \frac{94}{100}\right) - \left(3 + \frac{56}{100}\right) \cdot \left(3 + \frac{56}{100}\right) \cdot \left(3 + \frac{56}{100}\right) \cdot \frac{1}{8 + \frac{94}{100}} \cdot \left(8 + \frac{94}{100}\right) + \left(8 + \frac{94}{100}\right) \cdot \left(3 + \frac{56}{100}\right) + \left(3 + \frac{56}{100}\right) \cdot \left(3 + \frac{56}{100}\right)\\& = \frac{447}{50} \cdot \frac{447}{50} \cdot \left(8 + \frac{47}{50}\right) - \left(3 + \frac{56}{100}\right) \cdot \left(3 + \frac{56}{100}\right) \cdot \left(3 + \frac{56}{100}\right) \cdot \frac{1}{8 + \frac{94}{100}} \cdot \left(8 + \frac{94}{100}\right) + \left(8 + \frac{94}{100}\right) \cdot \left(3 + \frac{56}{100}\right) + \left(3 + \frac{56}{100}\right) \cdot \left(3 + \frac{56}{100}\right)\\& = \frac{447}{50} \cdot \frac{447}{50} \cdot \frac{447}{50} - \left(3 + \frac{56}{100}\right) \cdot \left(3 + \frac{56}{100}\right) \cdot \left(3 + \frac{56}{100}\right) \cdot \frac{1}{8 + \frac{94}{100}} \cdot \left(8 + \frac{94}{100}\right) + \left(8 + \frac{94}{100}\right) \cdot \left(3 + \frac{56}{100}\right) + \left(3 + \frac{56}{100}\right) \cdot \left(3 + \frac{56}{100}\right)\\& = \frac{199809}{2500} \cdot \frac{447}{50} - \left(3 + \frac{56}{100}\right) \cdot \left(3 + \frac{56}{100}\right) \cdot \left(3 + \frac{56}{100}\right) \cdot \frac{1}{8 + \frac{94}{100}} \cdot \left(8 + \frac{94}{100}\right) + \left(8 + \frac{94}{100}\right) \cdot \left(3 + \frac{56}{100}\right) + \left(3 + \frac{56}{100}\right) \cdot \left(3 + \frac{56}{100}\right)\\& = \frac{89314623}{125000} - \left(3 + \frac{56}{100}\right) \cdot \left(3 + \frac{56}{100}\right) \cdot \left(3 + \frac{56}{100}\right) \cdot \frac{1}{8 + \frac{94}{100}} \cdot \left(8 + \frac{94}{100}\right) + \left(8 + \frac{94}{100}\right) \cdot \left(3 + \frac{56}{100}\right) + \left(3 + \frac{56}{100}\right) \cdot \left(3 + \frac{56}{100}\right)\\& = \frac{89314623}{125000} - \left(3 + \frac{14}{25}\right) \cdot \left(3 + \frac{56}{100}\right) \cdot \left(3 + \frac{56}{100}\right) \cdot \frac{1}{8 + \frac{94}{100}} \cdot \left(8 + \frac{94}{100}\right) + \left(8 + \frac{94}{100}\right) \cdot \left(3 + \frac{56}{100}\right) + \left(3 + \frac{56}{100}\right) \cdot \left(3 + \frac{56}{100}\right)\\& = \frac{89314623}{125000} - \frac{89}{25} \cdot \left(3 + \frac{56}{100}\right) \cdot \left(3 + \frac{56}{100}\right) \cdot \frac{1}{8 + \frac{94}{100}} \cdot \left(8 + \frac{94}{100}\right) + \left(8 + \frac{94}{100}\right) \cdot \left(3 + \frac{56}{100}\right) + \left(3 + \frac{56}{100}\right) \cdot \left(3 + \frac{56}{100}\right)\\& = \frac{89314623}{125000} - \frac{89}{25} \cdot \left(3 + \frac{14}{25}\right) \cdot \left(3 + \frac{56}{100}\right) \cdot \frac{1}{8 + \frac{94}{100}} \cdot \left(8 + \frac{94}{100}\right) + \left(8 + \frac{94}{100}\right) \cdot \left(3 + \frac{56}{100}\right) + \left(3 + \frac{56}{100}\right) \cdot \left(3 + \frac{56}{100}\right)\\& = \frac{89314623}{125000} - \frac{89}{25} \cdot \frac{89}{25} \cdot \left(3 + \frac{56}{100}\right) \cdot \frac{1}{8 + \frac{94}{100}} \cdot \left(8 + \frac{94}{100}\right) + \left(8 + \frac{94}{100}\right) \cdot \left(3 + \frac{56}{100}\right) + \left(3 + \frac{56}{100}\right) \cdot \left(3 + \frac{56}{100}\right)\\& = \frac{89314623}{125000} - \frac{89}{25} \cdot \frac{89}{25} \cdot \left(3 + \frac{14}{25}\right) \cdot \frac{1}{8 + \frac{94}{100}} \cdot \left(8 + \frac{94}{100}\right) + \left(8 + \frac{94}{100}\right) \cdot \left(3 + \frac{56}{100}\right) + \left(3 + \frac{56}{100}\right) \cdot \left(3 + \frac{56}{100}\right)\\& = \frac{89314623}{125000} - \frac{89}{25} \cdot \frac{89}{25} \cdot \frac{89}{25} \cdot \frac{1}{8 + \frac{94}{100}} \cdot \left(8 + \frac{94}{100}\right) + \left(8 + \frac{94}{100}\right) \cdot \left(3 + \frac{56}{100}\right) + \left(3 + \frac{56}{100}\right) \cdot \left(3 + \frac{56}{100}\right)\\& = \frac{89314623}{125000} - \frac{89}{25} \cdot \frac{89}{25} \cdot \frac{89}{25} \cdot \frac{1}{8 + \frac{47}{50}} \cdot \left(8 + \frac{94}{100}\right) + \left(8 + \frac{94}{100}\right) \cdot \left(3 + \frac{56}{100}\right) + \left(3 + \frac{56}{100}\right) \cdot \left(3 + \frac{56}{100}\right)\\& = \frac{89314623}{125000} - \frac{89}{25} \cdot \frac{89}{25} \cdot \frac{89}{25} \cdot \frac{1}{\frac{447}{50}} \cdot \left(8 + \frac{94}{100}\right) + \left(8 + \frac{94}{100}\right) \cdot \left(3 + \frac{56}{100}\right) + \left(3 + \frac{56}{100}\right) \cdot \left(3 + \frac{56}{100}\right)\\& = \frac{89314623}{125000} - \frac{89}{25} \cdot \frac{89}{25} \cdot \frac{89}{25} \cdot \frac{50}{447} \cdot \left(8 + \frac{94}{100}\right) + \left(8 + \frac{94}{100}\right) \cdot \left(3 + \frac{56}{100}\right) + \left(3 + \frac{56}{100}\right) \cdot \left(3 + \frac{56}{100}\right)\\& = \frac{89314623}{125000} - \frac{89}{25} \cdot \frac{89}{25} \cdot \frac{89}{25} \cdot \frac{50}{447} \cdot \left(8 + \frac{47}{50}\right) + \left(8 + \frac{94}{100}\right) \cdot \left(3 + \frac{56}{100}\right) + \left(3 + \frac{56}{100}\right) \cdot \left(3 + \frac{56}{100}\right)\\& = \frac{89314623}{125000} - \frac{89}{25} \cdot \frac{89}{25} \cdot \frac{89}{25} \cdot \frac{50}{447} \cdot \frac{447}{50} + \left(8 + \frac{94}{100}\right) \cdot \left(3 + \frac{56}{100}\right) + \left(3 + \frac{56}{100}\right) \cdot \left(3 + \frac{56}{100}\right)\\& = \frac{89314623}{125000} - \frac{7921}{625} \cdot \frac{89}{25} \cdot \frac{50}{447} \cdot \frac{447}{50} + \left(8 + \frac{94}{100}\right) \cdot \left(3 + \frac{56}{100}\right) + \left(3 + \frac{56}{100}\right) \cdot \left(3 + \frac{56}{100}\right)\\& = \frac{89314623}{125000} - \frac{704969}{15625} \cdot \frac{50}{447} \cdot \frac{447}{50} + \left(8 + \frac{94}{100}\right) \cdot \left(3 + \frac{56}{100}\right) + \left(3 + \frac{56}{100}\right) \cdot \left(3 + \frac{56}{100}\right)\\& = \frac{89314623}{125000} - \frac{1409938}{279375} \cdot \frac{447}{50} + \left(8 + \frac{94}{100}\right) \cdot \left(3 + \frac{56}{100}\right) + \left(3 + \frac{56}{100}\right) \cdot \left(3 + \frac{56}{100}\right)\\& = \frac{89314623}{125000} - \frac{704969}{15625} + \left(8 + \frac{94}{100}\right) \cdot \left(3 + \frac{56}{100}\right) + \left(3 + \frac{56}{100}\right) \cdot \left(3 + \frac{56}{100}\right)\\& = \frac{89314623}{125000} - \frac{704969}{15625} + \left(8 + \frac{47}{50}\right) \cdot \left(3 + \frac{56}{100}\right) + \left(3 + \frac{56}{100}\right) \cdot \left(3 + \frac{56}{100}\right)\\& = \frac{89314623}{125000} - \frac{704969}{15625} + \frac{447}{50} \cdot \left(3 + \frac{56}{100}\right) + \left(3 + \frac{56}{100}\right) \cdot \left(3 + \frac{56}{100}\right)\\& = \frac{89314623}{125000} - \frac{704969}{15625} + \frac{447}{50} \cdot \left(3 + \frac{14}{25}\right) + \left(3 + \frac{56}{100}\right) \cdot \left(3 + \frac{56}{100}\right)\\& = \frac{89314623}{125000} - \frac{704969}{15625} + \frac{447}{50} \cdot \frac{89}{25} + \left(3 + \frac{56}{100}\right) \cdot \left(3 + \frac{56}{100}\right)\\& = \frac{89314623}{125000} - \frac{704969}{15625} + \frac{39783}{1250} + \left(3 + \frac{56}{100}\right) \cdot \left(3 + \frac{56}{100}\right)\\& = \frac{89314623}{125000} - \frac{704969}{15625} + \frac{39783}{1250} + \left(3 + \frac{14}{25}\right) \cdot \left(3 + \frac{56}{100}\right)\\& = \frac{89314623}{125000} - \frac{704969}{15625} + \frac{39783}{1250} + \frac{89}{25} \cdot \left(3 + \frac{56}{100}\right)\\& = \frac{89314623}{125000} - \frac{704969}{15625} + \frac{39783}{1250} + \frac{89}{25} \cdot \left(3 + \frac{14}{25}\right)\\& = \frac{89314623}{125000} - \frac{704969}{15625} + \frac{39783}{1250} + \frac{89}{25} \cdot \frac{89}{25}\\& = \frac{89314623}{125000} - \frac{704969}{15625} + \frac{39783}{1250} + \frac{7921}{625}\\& = \frac{83674871}{125000} + \frac{39783}{1250} + \frac{7921}{625}\\& = \frac{87653171}{125000} + \frac{7921}{625}\\& = \frac{89237371}{125000}\end{aligned}\]