Господин Экзамен
Раскрыть скобки в (-2+3*x^2)*(x^2+5)+2*x*(x^3-2*x+2)
Решение
Вы ввели
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/ 2\ / 2 \ / 3 \ \-2 + 3*x /*\x + 5/ + 2*x*\x - 2*x + 2/
$$2 x \left(x^{3} - 2 x + 2\right) + \left(x^{2} + 5\right) \left(3 x^{2} - 2\right)$$
(-2 + 3*x^2)*(x^2 + 5) + 2*x*(x^3 - 2*x + 2)
Общее упрощение
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4 2 -10 + 4*x + 5*x + 9*x
$$5 x^{4} + 9 x^{2} + 4 x - 10$$
-10 + 4*x + 5*x^4 + 9*x^2
Разложение на множители
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/ _________________ \ / _________________ \ / _________________ \
| / _______ / ___\ | | / _______ / ___\ | | / _______ |
| 1 / 77 \/ 44610 | 1 I*\/ 3 | 37 | | 1 / 77 \/ 44610 | 1 I*\/ 3 | 37 | | 1 / 77 \/ 44610 37 |
1*(x + 1)*|x + - - - 3 / --- + --------- *|- - - -------| + -----------------------------------------|*|x + - - - 3 / --- + --------- *|- - + -------| + -----------------------------------------|*|x + - - - 3 / --- + --------- + -------------------------|
| 3 \/ 135 225 \ 2 2 / _________________| | 3 \/ 135 225 \ 2 2 / _________________| | 3 \/ 135 225 _________________|
| / ___\ / _______ | | / ___\ / _______ | | / _______ |
| | 1 I*\/ 3 | / 77 \/ 44610 | | | 1 I*\/ 3 | / 77 \/ 44610 | | / 77 \/ 44610 |
| 45*|- - - -------|*3 / --- + --------- | | 45*|- - + -------|*3 / --- + --------- | | 45*3 / --- + --------- |
\ \ 2 2 / \/ 135 225 / \ \ 2 2 / \/ 135 225 / \ \/ 135 225 /
$$1 \left(x + 1\right) \left(x - \left(\frac{1}{3} + \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{77}{135} + \frac{\sqrt{44610}}{225}} - \frac{37}{45 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{77}{135} + \frac{\sqrt{44610}}{225}}}\right)\right) \left(x - \left(\frac{1}{3} - \frac{37}{45 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{77}{135} + \frac{\sqrt{44610}}{225}}} + \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{77}{135} + \frac{\sqrt{44610}}{225}}\right)\right) \left(x - \left(- \frac{37}{45 \sqrt[3]{\frac{77}{135} + \frac{\sqrt{44610}}{225}}} + \frac{1}{3} + \sqrt[3]{\frac{77}{135} + \frac{\sqrt{44610}}{225}}\right)\right)$$
(((1*(x + 1))*(x - (1/3 - (77/135 + sqrt(44610)/225)^(1/3)*(-1/2 - i*sqrt(3)/2) + 37/(45*(-1/2 - i*sqrt(3)/2)*(77/135 + sqrt(44610)/225)^(1/3)))))*(x - (1/3 - (77/135 + sqrt(44610)/225)^(1/3)*(-1/2 + i*sqrt(3)/2) + 37/(45*(-1/2 + i*sqrt(3)/2)*(77/135 + sqrt(44610)/225)^(1/3)))))*(x - (1/3 - (77/135 + sqrt(44610)/225)^(1/3) + 37/(45*(77/135 + sqrt(44610)/225)^(1/3))))
Численный ответ
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(5.0 + x^2)*(-2.0 + 3.0*x^2) + 2.0*x*(2.0 + x^3 - 2.0*x)
(5.0 + x^2)*(-2.0 + 3.0*x^2) + 2.0*x*(2.0 + x^3 - 2.0*x)
Рациональный знаменатель
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4 2 -10 + 4*x + 5*x + 9*x
$$5 x^{4} + 9 x^{2} + 4 x - 10$$
-10 + 4*x + 5*x^4 + 9*x^2
Общий знаменатель
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4 2 -10 + 4*x + 5*x + 9*x
$$5 x^{4} + 9 x^{2} + 4 x - 10$$
-10 + 4*x + 5*x^4 + 9*x^2
Комбинаторика
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/ 2 3 \ (1 + x)*\-10 - 5*x + 5*x + 14*x/
$$\left(x + 1\right) \left(5 x^{3} - 5 x^{2} + 14 x - 10\right)$$
(1 + x)*(-10 - 5*x^2 + 5*x^3 + 14*x)