Господин Экзамен
Раскрыть скобки в (m+3)*m2^2-(m^2-1)*m+4*(2-2*m^2)
Решение
Вы ввели
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2 / 2 \ / 2\ (m + 3)*m2 - \m - 1/*m + 4*\2 - 2*m /
$$m_{2}^{2} \left(m + 3\right) - m \left(m^{2} - 1\right) + 4 \cdot \left(- 2 m^{2} + 2\right)$$
(m + 3)*m2^2 - (m^2 - 1*1)*m + 4*(2 - 2*m^2)
Общее упрощение
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2 2 / 2\ 8 - 8*m + m2 *(3 + m) - m*\-1 + m /
$$m_{2}^{2} \left(m + 3\right) - 8 m^{2} - m \left(m^{2} - 1\right) + 8$$
8 - 8*m^2 + m2^2*(3 + m) - m*(-1 + m^2)
Разложение на множители
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/ ______________________________________________________ \ / ______________________________________________________ \ / ______________________________________________________ \ | / __________________________________ | | / __________________________________ | | / __________________________________ | | / / 2 3 | | / / 2 3 | | / / 2 3 | | / / / 2\ / 2\ 2 | | / / / 2\ / 2\ 2 / ___\ | | / / / 2\ / 2\ 2 / ___\ | | / \/ \880 - 9*m2 / - 4*\67 + 3*m2 / 9*m2 | | / \/ \880 - 9*m2 / - 4*\67 + 3*m2 / 9*m2 | 1 I*\/ 3 | | | / \/ \880 - 9*m2 / - 4*\67 + 3*m2 / 9*m2 | 1 I*\/ 3 | | | 3 / 440 + -------------------------------------- - ----- 2 | | 3 / 440 + -------------------------------------- - ----- *|- - - -------| 2 | | 3 / 440 + -------------------------------------- - ----- *|- - + -------| 2 | | 8 \/ 2 2 67 + 3*m2 | | 8 \/ 2 2 \ 2 2 / 67 + 3*m2 | | 8 \/ 2 2 \ 2 2 / 67 + 3*m2 | 1*|m + - + ------------------------------------------------------------- + ---------------------------------------------------------------|*|m + - + ----------------------------------------------------------------------------- + -------------------------------------------------------------------------------|*|m + - + ----------------------------------------------------------------------------- + -------------------------------------------------------------------------------| | 3 3 ______________________________________________________| | 3 3 ______________________________________________________| | 3 3 ______________________________________________________| | / __________________________________ | | / __________________________________ | | / __________________________________ | | / / 2 3 | | / / 2 3 | | / / 2 3 | | / / / 2\ / 2\ 2 | | / ___\ / / / 2\ / 2\ 2 | | / ___\ / / / 2\ / 2\ 2 | | / \/ \880 - 9*m2 / - 4*\67 + 3*m2 / 9*m2 | | | 1 I*\/ 3 | / \/ \880 - 9*m2 / - 4*\67 + 3*m2 / 9*m2 | | | 1 I*\/ 3 | / \/ \880 - 9*m2 / - 4*\67 + 3*m2 / 9*m2 | | 3*3 / 440 + -------------------------------------- - ----- | | 3*|- - - -------|*3 / 440 + -------------------------------------- - ----- | | 3*|- - + -------|*3 / 440 + -------------------------------------- - ----- | \ \/ 2 2 / \ \ 2 2 / \/ 2 2 / \ \ 2 2 / \/ 2 2 /
$$1 \left(m + \left(\frac{\sqrt[3]{- \frac{9 m_{2}^{2}}{2} + \frac{\sqrt{- 4 \left(3 m_{2}^{2} + 67\right)^{3} + \left(- 9 m_{2}^{2} + 880\right)^{2}}}{2} + 440}}{3} + \frac{3 m_{2}^{2} + 67}{3 \sqrt[3]{- \frac{9 m_{2}^{2}}{2} + \frac{\sqrt{- 4 \left(3 m_{2}^{2} + 67\right)^{3} + \left(- 9 m_{2}^{2} + 880\right)^{2}}}{2} + 440}} + \frac{8}{3}\right)\right) \left(m + \left(\frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- \frac{9 m_{2}^{2}}{2} + \frac{\sqrt{- 4 \left(3 m_{2}^{2} + 67\right)^{3} + \left(- 9 m_{2}^{2} + 880\right)^{2}}}{2} + 440}}{3} + \frac{3 m_{2}^{2} + 67}{3 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- \frac{9 m_{2}^{2}}{2} + \frac{\sqrt{- 4 \left(3 m_{2}^{2} + 67\right)^{3} + \left(- 9 m_{2}^{2} + 880\right)^{2}}}{2} + 440}} + \frac{8}{3}\right)\right) \left(m + \left(\frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- \frac{9 m_{2}^{2}}{2} + \frac{\sqrt{- 4 \left(3 m_{2}^{2} + 67\right)^{3} + \left(- 9 m_{2}^{2} + 880\right)^{2}}}{2} + 440}}{3} + \frac{3 m_{2}^{2} + 67}{3 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- \frac{9 m_{2}^{2}}{2} + \frac{\sqrt{- 4 \left(3 m_{2}^{2} + 67\right)^{3} + \left(- 9 m_{2}^{2} + 880\right)^{2}}}{2} + 440}} + \frac{8}{3}\right)\right)$$
((1*(m + (8/3 + (440 + sqrt((880 - 9*m2^2)^2 - 4*(67 + 3*m2^2)^3)/2 - 9*m2^2/2)^(1/3)/3 + (67 + 3*m2^2)/(3*(440 + sqrt((880 - 9*m2^2)^2 - 4*(67 + 3*m2^2)^3)/2 - 9*m2^2/2)^(1/3)))))*(m + (8/3 + (440 + sqrt((880 - 9*m2^2)^2 - 4*(67 + 3*m2^2)^3)/2 - 9*m2^2/2)^(1/3)*(-1/2 - i*sqrt(3)/2)/3 + (67 + 3*m2^2)/(3*(-1/2 - i*sqrt(3)/2)*(440 + sqrt((880 - 9*m2^2)^2 - 4*(67 + 3*m2^2)^3)/2 - 9*m2^2/2)^(1/3)))))*(m + (8/3 + (440 + sqrt((880 - 9*m2^2)^2 - 4*(67 + 3*m2^2)^3)/2 - 9*m2^2/2)^(1/3)*(-1/2 + i*sqrt(3)/2)/3 + (67 + 3*m2^2)/(3*(-1/2 + i*sqrt(3)/2)*(440 + sqrt((880 - 9*m2^2)^2 - 4*(67 + 3*m2^2)^3)/2 - 9*m2^2/2)^(1/3))))
Численный ответ
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8.0 - 8.0*m^2 + m2^2*(3.0 + m) - m*(-1.0 + m^2)
8.0 - 8.0*m^2 + m2^2*(3.0 + m) - m*(-1.0 + m^2)
Собрать выражение
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2 2 / 2\ 8 - 8*m + m2 *(3 + m) - m*\-1 + m /
$$m_{2}^{2} \left(m + 3\right) - 8 m^{2} - m \left(m^{2} - 1\right) + 8$$
2 / 2\ 2 8 - 8*m + m*\1 - m / + m2 *(3 + m)
$$m_{2}^{2} \left(m + 3\right) - 8 m^{2} + m \left(- m^{2} + 1\right) + 8$$
8 - 8*m^2 + m*(1 - m^2) + m2^2*(3 + m)
Степени
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2 2 / 2\ 8 - 8*m + m2 *(3 + m) - m*\-1 + m /
$$m_{2}^{2} \left(m + 3\right) - 8 m^{2} - m \left(m^{2} - 1\right) + 8$$
8 - 8*m^2 + m2^2*(3 + m) - m*(-1 + m^2)
Объединение рациональных выражений
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2 2 / 2\ 8 - 8*m + m2 *(3 + m) - m*\-1 + m /
$$m_{2}^{2} \left(m + 3\right) - 8 m^{2} - m \left(m^{2} - 1\right) + 8$$
8 - 8*m^2 + m2^2*(3 + m) - m*(-1 + m^2)
Комбинаторика
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3 2 2 2 8 + m - m - 8*m + 3*m2 + m*m2
$$- m^{3} + m m_{2}^{2} - 8 m^{2} + 3 m_{2}^{2} + m + 8$$
8 + m - m^3 - 8*m^2 + 3*m2^2 + m*m2^2
Общий знаменатель
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3 2 2 2 8 + m - m - 8*m + 3*m2 + m*m2
$$- m^{3} + m m_{2}^{2} - 8 m^{2} + 3 m_{2}^{2} + m + 8$$
8 + m - m^3 - 8*m^2 + 3*m2^2 + m*m2^2
Рациональный знаменатель
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3 2 2 2 8 + m - m - 8*m + 3*m2 + m*m2
$$- m^{3} + m m_{2}^{2} - 8 m^{2} + 3 m_{2}^{2} + m + 8$$
2 2 / 2\ 8 - 8*m + m2 *(3 + m) - m*\-1 + m /
$$m_{2}^{2} \left(m + 3\right) - 8 m^{2} - m \left(m^{2} - 1\right) + 8$$
8 - 8*m^2 + m2^2*(3 + m) - m*(-1 + m^2)