Господин Экзамен
Раскрыть скобки в (x+5)*(x^2-5*x+25)-x^2*(x^2+3)
Решение
Вы ввели
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/ 2 \ 2 / 2 \ (x + 5)*\x - 5*x + 25/ - x *\x + 3/
$$- x^{2} \left(x^{2} + 3\right) + \left(x + 5\right) \left(x^{2} - 5 x + 25\right)$$
(x + 5)*(x^2 - 5*x + 25) - x^2*(x^2 + 3)
Общее упрощение
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3 4 2 125 + x - x - 3*x
$$- x^{4} + x^{3} - 3 x^{2} + 125$$
125 + x^3 - x^4 - 3*x^2
Разложение на множители
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- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + -------------------------------------------------------------------------------|*|x + - - - ------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*|x + - - - ------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*|x + - - + ------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------| \ 4 2 2 / \ 4 2 2 / \ 4 2 2 / \ 4 2 2 /
$$\left(x - \left(\frac{\sqrt{- \frac{497}{6 \sqrt[3]{\frac{877}{16} + \frac{5 \sqrt{61418445}}{144}}} - \frac{7}{4} + 2 \sqrt[3]{\frac{877}{16} + \frac{5 \sqrt{61418445}}{144}}}}{2} + \frac{1}{4} - \frac{\sqrt{- \frac{11}{4 \sqrt{- \frac{497}{6 \sqrt[3]{\frac{877}{16} + \frac{5 \sqrt{61418445}}{144}}} - \frac{7}{4} + 2 \sqrt[3]{\frac{877}{16} + \frac{5 \sqrt{61418445}}{144}}}} - 2 \sqrt[3]{\frac{877}{16} + \frac{5 \sqrt{61418445}}{144}} - \frac{7}{2} + \frac{497}{6 \sqrt[3]{\frac{877}{16} + \frac{5 \sqrt{61418445}}{144}}}}}{2}\right)\right) 1 \left(x - \left(- \frac{\sqrt{- \frac{497}{6 \sqrt[3]{\frac{877}{16} + \frac{5 \sqrt{61418445}}{144}}} - \frac{7}{4} + 2 \sqrt[3]{\frac{877}{16} + \frac{5 \sqrt{61418445}}{144}}}}{2} + \frac{1}{4} + \frac{\sqrt{- 2 \sqrt[3]{\frac{877}{16} + \frac{5 \sqrt{61418445}}{144}} - \frac{7}{2} + \frac{497}{6 \sqrt[3]{\frac{877}{16} + \frac{5 \sqrt{61418445}}{144}}} + \frac{11}{4 \sqrt{- \frac{497}{6 \sqrt[3]{\frac{877}{16} + \frac{5 \sqrt{61418445}}{144}}} - \frac{7}{4} + 2 \sqrt[3]{\frac{877}{16} + \frac{5 \sqrt{61418445}}{144}}}}}}{2}\right)\right) \left(x - \left(\frac{\sqrt{- \frac{497}{6 \sqrt[3]{\frac{877}{16} + \frac{5 \sqrt{61418445}}{144}}} - \frac{7}{4} + 2 \sqrt[3]{\frac{877}{16} + \frac{5 \sqrt{61418445}}{144}}}}{2} + \frac{1}{4} + \frac{\sqrt{- \frac{11}{4 \sqrt{- \frac{497}{6 \sqrt[3]{\frac{877}{16} + \frac{5 \sqrt{61418445}}{144}}} - \frac{7}{4} + 2 \sqrt[3]{\frac{877}{16} + \frac{5 \sqrt{61418445}}{144}}}} - 2 \sqrt[3]{\frac{877}{16} + \frac{5 \sqrt{61418445}}{144}} - \frac{7}{2} + \frac{497}{6 \sqrt[3]{\frac{877}{16} + \frac{5 \sqrt{61418445}}{144}}}}}{2}\right)\right) \left(x + \left(- \frac{1}{4} + \frac{\sqrt{- \frac{497}{6 \sqrt[3]{\frac{877}{16} + \frac{5 \sqrt{61418445}}{144}}} - \frac{7}{4} + 2 \sqrt[3]{\frac{877}{16} + \frac{5 \sqrt{61418445}}{144}}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{\frac{877}{16} + \frac{5 \sqrt{61418445}}{144}} - \frac{7}{2} + \frac{497}{6 \sqrt[3]{\frac{877}{16} + \frac{5 \sqrt{61418445}}{144}}} + \frac{11}{4 \sqrt{- \frac{497}{6 \sqrt[3]{\frac{877}{16} + \frac{5 \sqrt{61418445}}{144}}} - \frac{7}{4} + 2 \sqrt[3]{\frac{877}{16} + \frac{5 \sqrt{61418445}}{144}}}}}}{2}\right)\right)$$
(((1*(x - (1/4 - sqrt(-7/2 - 2*(877/16 + 5*sqrt(61418445)/144)^(1/3) + 11/(4*sqrt(-7/4 + 2*(877/16 + 5*sqrt(61418445)/144)^(1/3) - 497/(6*(877/16 + 5*sqrt(61418445)/144)^(1/3)))) + 497/(6*(877/16 + 5*sqrt(61418445)/144)^(1/3)))/2 + sqrt(-7/4 + 2*(877/16 + 5*sqrt(61418445)/144)^(1/3) - 497/(6*(877/16 + 5*sqrt(61418445)/144)^(1/3)))/2)))*(x - (1/4 - sqrt(-7/4 + 2*(877/16 + 5*sqrt(61418445)/144)^(1/3) - 497/(6*(877/16 + 5*sqrt(61418445)/144)^(1/3)))/2 + sqrt(-7/2 - 2*(877/16 + 5*sqrt(61418445)/144)^(1/3) - 11/(4*sqrt(-7/4 + 2*(877/16 + 5*sqrt(61418445)/144)^(1/3) - 497/(6*(877/16 + 5*sqrt(61418445)/144)^(1/3)))) + 497/(6*(877/16 + 5*sqrt(61418445)/144)^(1/3)))/2)))*(x - (1/4 - sqrt(-7/4 + 2*(877/16 + 5*sqrt(61418445)/144)^(1/3) - 497/(6*(877/16 + 5*sqrt(61418445)/144)^(1/3)))/2 - sqrt(-7/2 - 2*(877/16 + 5*sqrt(61418445)/144)^(1/3) - 11/(4*sqrt(-7/4 + 2*(877/16 + 5*sqrt(61418445)/144)^(1/3) - 497/(6*(877/16 + 5*sqrt(61418445)/144)^(1/3)))) + 497/(6*(877/16 + 5*sqrt(61418445)/144)^(1/3)))/2)))*(x - (1/4 + sqrt(-7/4 + 2*(877/16 + 5*sqrt(61418445)/144)^(1/3) - 497/(6*(877/16 + 5*sqrt(61418445)/144)^(1/3)))/2 + sqrt(-7/2 - 2*(877/16 + 5*sqrt(61418445)/144)^(1/3) + 11/(4*sqrt(-7/4 + 2*(877/16 + 5*sqrt(61418445)/144)^(1/3) - 497/(6*(877/16 + 5*sqrt(61418445)/144)^(1/3)))) + 497/(6*(877/16 + 5*sqrt(61418445)/144)^(1/3)))/2))
Численный ответ
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(5.0 + x)*(25.0 + x^2 - 5.0*x) - x^2*(3.0 + x^2)
(5.0 + x)*(25.0 + x^2 - 5.0*x) - x^2*(3.0 + x^2)
Комбинаторика
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3 4 2 125 + x - x - 3*x
$$- x^{4} + x^{3} - 3 x^{2} + 125$$
125 + x^3 - x^4 - 3*x^2
Степени
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2 / 2\ / 2 \ x *\-3 - x / + (5 + x)*\25 + x - 5*x/
$$x^{2} \left(- x^{2} - 3\right) + \left(x + 5\right) \left(x^{2} - 5 x + 25\right)$$
x^2*(-3 - x^2) + (5 + x)*(25 + x^2 - 5*x)
Общий знаменатель
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3 4 2 125 + x - x - 3*x
$$- x^{4} + x^{3} - 3 x^{2} + 125$$
125 + x^3 - x^4 - 3*x^2
Рациональный знаменатель
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3 4 2 125 + x - x - 3*x
$$- x^{4} + x^{3} - 3 x^{2} + 125$$
125 + x^3 - x^4 - 3*x^2