9^2-m^2*(3^2+m^2)-(m-2)*(m+2)^2еслиm=4 (упростите выражение)

Вы ввели

 2    2 / 2    2\                  2
9  - m *\3  + m / - (m - 2)*(m + 2) 

$$- m^{2} \left(m^{2} + 3^{2}\right) - \left(m + 2\right)^{2} \left(m - 2\right) + 9^{2}$$

Подстановка условия

9^2 - m^2*(3^2 + m^2) - (m - 1*2)*(m + 2)^2 при m = 4

подставляем

 2    2 / 2    2\                  2
9  - m *\3  + m / - (m - 2)*(m + 2) 

$$- m^{2} \left(m^{2} + 3^{2}\right) - \left(m + 2\right)^{2} \left(m - 2\right) + 9^{2}$$

      3    4       2      
89 - m  - m  - 11*m  + 4*m

$$- m^{4} - m^{3} - 11 m^{2} + 4 m + 89$$

переменные

m = 4

$$m = 4$$

        3      4         2        
89 - (4)  - (4)  - 11*(4)  + 4*(4)

$$- (4)^{4} - (4)^{3} - 11 (4)^{2} + 4 (4) + 89$$

      3    4       2      
89 - 4  - 4  - 11*4  + 4*4

$$- 4^{4} - 11 \cdot 4^{2} - 4^{3} + 4 \cdot 4 + 89$$

-391

$$-391$$

Степени

      2 /     2\          2         
81 - m *\9 + m / - (2 + m) *(-2 + m)

$$- m^{2} \left(m^{2} + 9\right) - \left(m - 2\right) \left(m + 2\right)^{2} + 81$$

      2 /      2\          2        
81 + m *\-9 - m / + (2 + m) *(2 - m)

$$m^{2} \left(- m^{2} - 9\right) + \left(2 - m\right) \left(m + 2\right)^{2} + 81$$

      2 /      2\          2        
81 + m *\-9 - m / + (m + 2) *(2 - m)

$$m^{2} \left(- m^{2} - 9\right) + \left(2 - m\right) \left(m + 2\right)^{2} + 81$$

Численный ответ

81.0 - m^2*(9.0 + m^2) - 4.0*(1 + 0.5*m)^2*(-2.0 + m)

Рациональный знаменатель

      2 /     2\          2         
81 - m *\9 + m / - (2 + m) *(-2 + m)

$$- m^{2} \left(m^{2} + 9\right) - \left(m - 2\right) \left(m + 2\right)^{2} + 81$$

      4      2            2            2
81 - m  - 9*m  + 2*(2 + m)  - m*(2 + m) 

$$- m^{4} - 9 m^{2} - m \left(m + 2\right)^{2} + 2 \left(m + 2\right)^{2} + 81$$

Объединение рациональных выражений

      2 /     2\          2         
81 - m *\9 + m / - (2 + m) *(-2 + m)

$$- m^{2} \left(m^{2} + 9\right) - \left(m - 2\right) \left(m + 2\right)^{2} + 81$$

Общее упрощение

      3    4       2      
89 - m  - m  - 11*m  + 4*m

$$- m^{4} - m^{3} - 11 m^{2} + 4 m + 89$$

Собрать выражение

      2 /     2\          2         
81 - m *\9 + m / - (2 + m) *(-2 + m)

$$- m^{2} \left(m^{2} + 9\right) - \left(m - 2\right) \left(m + 2\right)^{2} + 81$$

Общий знаменатель

      3    4       2      
89 - m  - m  - 11*m  + 4*m

$$- m^{4} - m^{3} - 11 m^{2} + 4 m + 89$$

Тригонометрическая часть

      2 /     2\          2         
81 - m *\9 + m / - (2 + m) *(-2 + m)

$$- m^{2} \left(m^{2} + 9\right) - \left(m - 2\right) \left(m + 2\right)^{2} + 81$$

Комбинаторика

      3    4       2      
89 - m  - m  - 11*m  + 4*m

$$- m^{4} - m^{3} - 11 m^{2} + 4 m + 89$$

Разложение на множители

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$$\left(m + \left(\frac{\sqrt{- \frac{935}{18 \sqrt[3]{\frac{71575}{432} + \frac{5 \sqrt{4144485}}{48}}} - \frac{85}{12} + 2 \sqrt[3]{\frac{71575}{432} + \frac{5 \sqrt{4144485}}{48}}}}{2} + \frac{1}{4} - \frac{\sqrt{- \frac{75}{4 \sqrt{- \frac{935}{18 \sqrt[3]{\frac{71575}{432} + \frac{5 \sqrt{4144485}}{48}}} - \frac{85}{12} + 2 \sqrt[3]{\frac{71575}{432} + \frac{5 \sqrt{4144485}}{48}}}} - 2 \sqrt[3]{\frac{71575}{432} + \frac{5 \sqrt{4144485}}{48}} - \frac{85}{6} + \frac{935}{18 \sqrt[3]{\frac{71575}{432} + \frac{5 \sqrt{4144485}}{48}}}}}{2}\right)\right) 1 \left(m + \left(\frac{\sqrt{- \frac{935}{18 \sqrt[3]{\frac{71575}{432} + \frac{5 \sqrt{4144485}}{48}}} - \frac{85}{12} + 2 \sqrt[3]{\frac{71575}{432} + \frac{5 \sqrt{4144485}}{48}}}}{2} + \frac{1}{4} + \frac{\sqrt{- \frac{75}{4 \sqrt{- \frac{935}{18 \sqrt[3]{\frac{71575}{432} + \frac{5 \sqrt{4144485}}{48}}} - \frac{85}{12} + 2 \sqrt[3]{\frac{71575}{432} + \frac{5 \sqrt{4144485}}{48}}}} - 2 \sqrt[3]{\frac{71575}{432} + \frac{5 \sqrt{4144485}}{48}} - \frac{85}{6} + \frac{935}{18 \sqrt[3]{\frac{71575}{432} + \frac{5 \sqrt{4144485}}{48}}}}}{2}\right)\right) \left(m - \left(- \frac{1}{4} + \frac{\sqrt{- \frac{935}{18 \sqrt[3]{\frac{71575}{432} + \frac{5 \sqrt{4144485}}{48}}} - \frac{85}{12} + 2 \sqrt[3]{\frac{71575}{432} + \frac{5 \sqrt{4144485}}{48}}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{\frac{71575}{432} + \frac{5 \sqrt{4144485}}{48}} - \frac{85}{6} + \frac{935}{18 \sqrt[3]{\frac{71575}{432} + \frac{5 \sqrt{4144485}}{48}}} + \frac{75}{4 \sqrt{- \frac{935}{18 \sqrt[3]{\frac{71575}{432} + \frac{5 \sqrt{4144485}}{48}}} - \frac{85}{12} + 2 \sqrt[3]{\frac{71575}{432} + \frac{5 \sqrt{4144485}}{48}}}}}}{2}\right)\right) \left(m + \left(- \frac{\sqrt{- \frac{935}{18 \sqrt[3]{\frac{71575}{432} + \frac{5 \sqrt{4144485}}{48}}} - \frac{85}{12} + 2 \sqrt[3]{\frac{71575}{432} + \frac{5 \sqrt{4144485}}{48}}}}{2} + \frac{1}{4} + \frac{\sqrt{- 2 \sqrt[3]{\frac{71575}{432} + \frac{5 \sqrt{4144485}}{48}} - \frac{85}{6} + \frac{935}{18 \sqrt[3]{\frac{71575}{432} + \frac{5 \sqrt{4144485}}{48}}} + \frac{75}{4 \sqrt{- \frac{935}{18 \sqrt[3]{\frac{71575}{432} + \frac{5 \sqrt{4144485}}{48}}} - \frac{85}{12} + 2 \sqrt[3]{\frac{71575}{432} + \frac{5 \sqrt{4144485}}{48}}}}}}{2}\right)\right)$$