Господин Экзамен
Раскрыть скобки в (2*x+1-0)*(x^3+1)-(3*x^2)*(x^2+x-1)
Решение
Вы ввели
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/ 3 \ 2 / 2 \ (2*x + 1 - 0)*\x + 1/ - 3*x *\x + x - 1/
$$- 3 x^{2} \left(x^{2} + x - 1\right) + \left(x^{3} + 1\right) \left(2 x - 0 + 1\right)$$
(2*x + 1 - 1*0)*(x^3 + 1) - 3*x^2*(x^2 + x - 1*1)
Общее упрощение
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4 3 2 1 - x - 2*x + 2*x + 3*x
$$- x^{4} - 2 x^{3} + 3 x^{2} + 2 x + 1$$
1 - x^4 - 2*x^3 + 2*x + 3*x^2
Разложение на множители
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/ _______________________________________________________________________________________________________________ \ / _______________________________________________________________________________________________________________\ / _______________________________________________________________________________________________________________\ / _______________________________________________________________________________________________________________\ | / _____________ | | / _____________ | | / _____________ | | / _____________ | | / / ___ | | / / ___ | | / / ___ | | / / ___ | | / / 7 \/ 3 4 1 | | / 4 / 7 \/ 3 1 | | / 4 / 7 \/ 3 1 | | / / 7 \/ 3 4 1 | | / 6 - 2*3 / - - + ----- + ----------------------------------------------------------- - -------------------- | | / 6 - ----------------------------------------------------------- - 2*3 / - - + ----- - -------------------- | | / 6 - ----------------------------------------------------------- - 2*3 / - - + ----- - -------------------- | | / 6 - 2*3 / - - + ----- + ----------------------------------------------------------- - -------------------- | | / \/ 8 2 _________________________________________________ _____________ _________________________________________________| | _________________________________________________ / _________________________________________________ \/ 8 2 _____________ | | _________________________________________________ / _________________________________________________ \/ 8 2 _____________ | | _________________________________________________ / \/ 8 2 _________________________________________________ _____________ | | / / _____________ / ___ / _____________ | | / _____________ / / _____________ / ___ | | / _____________ / / _____________ / ___ | | / _____________ / / _____________ / ___ | | / / / ___ / 7 \/ 3 / / ___ | | / / ___ / / / ___ / 7 \/ 3 | | / / ___ / / / ___ / 7 \/ 3 | | / / ___ / / / ___ / 7 \/ 3 | | / / 1 / 7 \/ 3 2*3 / - - + ----- / 1 / 7 \/ 3 | | / 1 / 7 \/ 3 / / 1 / 7 \/ 3 2*3 / - - + ----- | | / 1 / 7 \/ 3 / / 1 / 7 \/ 3 2*3 / - - + ----- | | / 1 / 7 \/ 3 / / 1 / 7 \/ 3 2*3 / - - + ----- | | / / 3 + -------------------- + 2*3 / - - + ----- \/ 8 2 / 3 + -------------------- + 2*3 / - - + ----- | | / 3 + -------------------- + 2*3 / - - + ----- / / 3 + -------------------- + 2*3 / - - + ----- \/ 8 2 | | / 3 + -------------------- + 2*3 / - - + ----- / / 3 + -------------------- + 2*3 / - - + ----- \/ 8 2 | | / 3 + -------------------- + 2*3 / - - + ----- / / 3 + -------------------- + 2*3 / - - + ----- \/ 8 2 | | / / _____________ \/ 8 2 / _____________ \/ 8 2 | | / _____________ \/ 8 2 / / _____________ \/ 8 2 | | / _____________ \/ 8 2 / / _____________ \/ 8 2 | | / _____________ \/ 8 2 / / _____________ \/ 8 2 | | / / / ___ / / ___ | | / / ___ / / / ___ | | / / ___ / / / ___ | | / / ___ / / / ___ | | / / / 7 \/ 3 / / 7 \/ 3 | | / / 7 \/ 3 / / / 7 \/ 3 | | / / 7 \/ 3 / / / 7 \/ 3 | | / / 7 \/ 3 / / / 7 \/ 3 | | / / 2*3 / - - + ----- / 2*3 / - - + ----- | | / 2*3 / - - + ----- / / 2*3 / - - + ----- | | / 2*3 / - - + ----- / / 2*3 / - - + ----- | | / 2*3 / - - + ----- / / 2*3 / - - + ----- | | 1 \/ \/ \/ 8 2 \/ \/ 8 2 | | 1 \/ \/ 8 2 \/ \/ \/ 8 2 | | 1 \/ \/ 8 2 \/ \/ \/ 8 2 | | 1 \/ \/ 8 2 \/ \/ \/ 8 2 | 1*|x + - - ------------------------------------------------------------------------------------------------------------------------------ + -----------------------------------------------------------|*|x + - - ----------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------|*|x + - - ----------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------|*|x + - + ----------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------| \ 2 2 2 / \ 2 2 2 / \ 2 2 2 / \ 2 2 2 /
$$\left(x - \left(- \frac{1}{2} + \frac{\sqrt{3 + \frac{1}{2 \sqrt[3]{- \frac{7}{8} + \frac{\sqrt{3}}{2}}} + 2 \sqrt[3]{- \frac{7}{8} + \frac{\sqrt{3}}{2}}}}{2} + \frac{\sqrt{6 - 2 \sqrt[3]{- \frac{7}{8} + \frac{\sqrt{3}}{2}} - \frac{4}{\sqrt{3 + \frac{1}{2 \sqrt[3]{- \frac{7}{8} + \frac{\sqrt{3}}{2}}} + 2 \sqrt[3]{- \frac{7}{8} + \frac{\sqrt{3}}{2}}}} - \frac{1}{2 \sqrt[3]{- \frac{7}{8} + \frac{\sqrt{3}}{2}}}}}{2}\right)\right) 1 \left(x + \left(\frac{1}{2} - \frac{\sqrt{6 - 2 \sqrt[3]{- \frac{7}{8} + \frac{\sqrt{3}}{2}} + \frac{4}{\sqrt{3 + \frac{1}{2 \sqrt[3]{- \frac{7}{8} + \frac{\sqrt{3}}{2}}} + 2 \sqrt[3]{- \frac{7}{8} + \frac{\sqrt{3}}{2}}}} - \frac{1}{2 \sqrt[3]{- \frac{7}{8} + \frac{\sqrt{3}}{2}}}}}{2} + \frac{\sqrt{3 + \frac{1}{2 \sqrt[3]{- \frac{7}{8} + \frac{\sqrt{3}}{2}}} + 2 \sqrt[3]{- \frac{7}{8} + \frac{\sqrt{3}}{2}}}}{2}\right)\right) \left(x + \left(\frac{1}{2} - \frac{\sqrt{3 + \frac{1}{2 \sqrt[3]{- \frac{7}{8} + \frac{\sqrt{3}}{2}}} + 2 \sqrt[3]{- \frac{7}{8} + \frac{\sqrt{3}}{2}}}}{2} + \frac{\sqrt{6 - 2 \sqrt[3]{- \frac{7}{8} + \frac{\sqrt{3}}{2}} - \frac{4}{\sqrt{3 + \frac{1}{2 \sqrt[3]{- \frac{7}{8} + \frac{\sqrt{3}}{2}}} + 2 \sqrt[3]{- \frac{7}{8} + \frac{\sqrt{3}}{2}}}} - \frac{1}{2 \sqrt[3]{- \frac{7}{8} + \frac{\sqrt{3}}{2}}}}}{2}\right)\right) \left(x + \left(\frac{1}{2} + \frac{\sqrt{3 + \frac{1}{2 \sqrt[3]{- \frac{7}{8} + \frac{\sqrt{3}}{2}}} + 2 \sqrt[3]{- \frac{7}{8} + \frac{\sqrt{3}}{2}}}}{2} + \frac{\sqrt{6 - 2 \sqrt[3]{- \frac{7}{8} + \frac{\sqrt{3}}{2}} + \frac{4}{\sqrt{3 + \frac{1}{2 \sqrt[3]{- \frac{7}{8} + \frac{\sqrt{3}}{2}}} + 2 \sqrt[3]{- \frac{7}{8} + \frac{\sqrt{3}}{2}}}} - \frac{1}{2 \sqrt[3]{- \frac{7}{8} + \frac{\sqrt{3}}{2}}}}}{2}\right)\right)$$
(((1*(x + (1/2 - sqrt(6 - 2*(-7/8 + sqrt(3)/2)^(1/3) + 4/sqrt(3 + 1/(2*(-7/8 + sqrt(3)/2)^(1/3)) + 2*(-7/8 + sqrt(3)/2)^(1/3)) - 1/(2*(-7/8 + sqrt(3)/2)^(1/3)))/2 + sqrt(3 + 1/(2*(-7/8 + sqrt(3)/2)^(1/3)) + 2*(-7/8 + sqrt(3)/2)^(1/3))/2)))*(x + (1/2 - sqrt(3 + 1/(2*(-7/8 + sqrt(3)/2)^(1/3)) + 2*(-7/8 + sqrt(3)/2)^(1/3))/2 - sqrt(6 - 4/sqrt(3 + 1/(2*(-7/8 + sqrt(3)/2)^(1/3)) + 2*(-7/8 + sqrt(3)/2)^(1/3)) - 2*(-7/8 + sqrt(3)/2)^(1/3) - 1/(2*(-7/8 + sqrt(3)/2)^(1/3)))/2)))*(x + (1/2 - sqrt(3 + 1/(2*(-7/8 + sqrt(3)/2)^(1/3)) + 2*(-7/8 + sqrt(3)/2)^(1/3))/2 + sqrt(6 - 4/sqrt(3 + 1/(2*(-7/8 + sqrt(3)/2)^(1/3)) + 2*(-7/8 + sqrt(3)/2)^(1/3)) - 2*(-7/8 + sqrt(3)/2)^(1/3) - 1/(2*(-7/8 + sqrt(3)/2)^(1/3)))/2)))*(x + (1/2 + sqrt(3 + 1/(2*(-7/8 + sqrt(3)/2)^(1/3)) + 2*(-7/8 + sqrt(3)/2)^(1/3))/2 + sqrt(6 - 2*(-7/8 + sqrt(3)/2)^(1/3) + 4/sqrt(3 + 1/(2*(-7/8 + sqrt(3)/2)^(1/3)) + 2*(-7/8 + sqrt(3)/2)^(1/3)) - 1/(2*(-7/8 + sqrt(3)/2)^(1/3)))/2))
Общий знаменатель
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4 3 2 1 - x - 2*x + 2*x + 3*x
$$- x^{4} - 2 x^{3} + 3 x^{2} + 2 x + 1$$
1 - x^4 - 2*x^3 + 2*x + 3*x^2
Численный ответ
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(1.0 + x^3)*(1.0 + 2.0*x) - 3.0*x^2*(-1.0 + x + x^2)
(1.0 + x^3)*(1.0 + 2.0*x) - 3.0*x^2*(-1.0 + x + x^2)
Рациональный знаменатель
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4 3 2 1 - x - 2*x + 2*x + 3*x
$$- x^{4} - 2 x^{3} + 3 x^{2} + 2 x + 1$$
/ 3\ 2 / 2\ \1 + x /*(1 + 2*x) - 3*x *\-1 + x + x /
$$- 3 x^{2} \left(x^{2} + x - 1\right) + \left(2 x + 1\right) \left(x^{3} + 1\right)$$
(1 + x^3)*(1 + 2*x) - 3*x^2*(-1 + x + x^2)
Собрать выражение
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/ 3\ 2 / 2\ \1 + x /*(1 + 2*x) - 3*x *\-1 + x + x /
$$- 3 x^{2} \left(x^{2} + x - 1\right) + \left(2 x + 1\right) \left(x^{3} + 1\right)$$
(1 + x^3)*(1 + 2*x) - 3*x^2*(-1 + x + x^2)
Степени
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/ 3\ 2 / 2\ \1 + x /*(1 + 2*x) - 3*x *\-1 + x + x /
$$- 3 x^{2} \left(x^{2} + x - 1\right) + \left(2 x + 1\right) \left(x^{3} + 1\right)$$
2 / 2\ / 3\ x *\3 - 3*x - 3*x / + \1 + x /*(1 + 2*x)
$$x^{2} \left(- 3 x^{2} - 3 x + 3\right) + \left(2 x + 1\right) \left(x^{3} + 1\right)$$
x^2*(3 - 3*x - 3*x^2) + (1 + x^3)*(1 + 2*x)
Комбинаторика
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4 3 2 1 - x - 2*x + 2*x + 3*x
$$- x^{4} - 2 x^{3} + 3 x^{2} + 2 x + 1$$
1 - x^4 - 2*x^3 + 2*x + 3*x^2
Объединение рациональных выражений
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/ 3\ 2 / 2\ \1 + x /*(1 + 2*x) - 3*x *\-1 + x + x /
$$- 3 x^{2} \left(x^{2} + x - 1\right) + \left(2 x + 1\right) \left(x^{3} + 1\right)$$
(1 + x^3)*(1 + 2*x) - 3*x^2*(-1 + x + x^2)