Господин Экзамен
Раскрыть скобки в (m^3+n^2)*(m^6-m^3*n^2+n^4)
Решение
Вы ввели
[src]
/ 3 2\ / 6 3 2 4\ \m + n /*\m - m *n + n /
$$\left(m^{3} + n^{2}\right) \left(m^{6} - m^{3} n^{2} + n^{4}\right)$$
(m^3 + n^2)*(m^6 - m^3*n^2 + n^4)
Разложение на множители
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/ _________________ _________________\ / _________________ _________________\ / _________________ _________________\ / _________________ _________________\
| / 2 ___ 2 / 2 ___ 2 | | / 2 ___ 2 / 2 ___ 2 | | / 2 ___ 2 / 2 ___ 2 | | / 2 ___ 2 / 2 ___ 2 |
/ _________________\ / _________________\ / _____ _____\ / _____ _____\ | / n I*\/ 3 *n ___ / n I*\/ 3 *n | | / n I*\/ 3 *n ___ / n I*\/ 3 *n | | / n I*\/ 3 *n ___ / n I*\/ 3 *n | | / n I*\/ 3 *n ___ / n I*\/ 3 *n |
/ _____\ | / 2 ___ 2 | | / 2 ___ 2 | | 3 / 2 ___ 3 / 2 | | 3 / 2 ___ 3 / 2 | | 3 / -- - ---------- I*\/ 3 *3 / -- - ---------- | | 3 / -- - ---------- I*\/ 3 *3 / -- - ---------- | | 3 / -- + ---------- I*\/ 3 *3 / -- + ---------- | | 3 / -- + ---------- I*\/ 3 *3 / -- + ---------- |
| 3 / 2 | | / n I*\/ 3 *n | | / n I*\/ 3 *n | | \/ -n I*\/ 3 *\/ -n | | \/ -n I*\/ 3 *\/ -n | | \/ 2 2 \/ 2 2 | | \/ 2 2 \/ 2 2 | | \/ 2 2 \/ 2 2 | | \/ 2 2 \/ 2 2 |
1*\m - \/ -n /*|m - 3 / -- - ---------- |*|m - 3 / -- + ---------- |*|m + -------- + ----------------|*|m + -------- - ----------------|*|m + ---------------------- + ------------------------------|*|m + ---------------------- - ------------------------------|*|m + ---------------------- + ------------------------------|*|m + ---------------------- - ------------------------------|
\ \/ 2 2 / \ \/ 2 2 / \ 2 2 / \ 2 2 / \ 2 2 / \ 2 2 / \ 2 2 / \ 2 2 /
$$1 \left(m - \sqrt[3]{- n^{2}}\right) \left(m - \sqrt[3]{\frac{n^{2}}{2} - \frac{\sqrt{3} i n^{2}}{2}}\right) \left(m - \sqrt[3]{\frac{n^{2}}{2} + \frac{\sqrt{3} i n^{2}}{2}}\right) \left(m + \left(\frac{\sqrt[3]{- n^{2}}}{2} + \frac{\sqrt{3} i \sqrt[3]{- n^{2}}}{2}\right)\right) \left(m + \left(\frac{\sqrt[3]{- n^{2}}}{2} - \frac{\sqrt{3} i \sqrt[3]{- n^{2}}}{2}\right)\right) \left(m + \left(\frac{\sqrt[3]{\frac{n^{2}}{2} - \frac{\sqrt{3} i n^{2}}{2}}}{2} + \frac{\sqrt{3} i \sqrt[3]{\frac{n^{2}}{2} - \frac{\sqrt{3} i n^{2}}{2}}}{2}\right)\right) \left(m + \left(\frac{\sqrt[3]{\frac{n^{2}}{2} - \frac{\sqrt{3} i n^{2}}{2}}}{2} - \frac{\sqrt{3} i \sqrt[3]{\frac{n^{2}}{2} - \frac{\sqrt{3} i n^{2}}{2}}}{2}\right)\right) \left(m + \left(\frac{\sqrt[3]{\frac{n^{2}}{2} + \frac{\sqrt{3} i n^{2}}{2}}}{2} + \frac{\sqrt{3} i \sqrt[3]{\frac{n^{2}}{2} + \frac{\sqrt{3} i n^{2}}{2}}}{2}\right)\right) \left(m + \left(\frac{\sqrt[3]{\frac{n^{2}}{2} + \frac{\sqrt{3} i n^{2}}{2}}}{2} - \frac{\sqrt{3} i \sqrt[3]{\frac{n^{2}}{2} + \frac{\sqrt{3} i n^{2}}{2}}}{2}\right)\right)$$
((((((((1*(m - (-n^2)^(1/3)))*(m - (n^2/2 - i*sqrt(3)*n^2/2)^(1/3)))*(m - (n^2/2 + i*sqrt(3)*n^2/2)^(1/3)))*(m + ((-n^2)^(1/3)/2 + i*sqrt(3)*(-n^2)^(1/3)/2)))*(m + ((-n^2)^(1/3)/2 - i*sqrt(3)*(-n^2)^(1/3)/2)))*(m + ((n^2/2 - i*sqrt(3)*n^2/2)^(1/3)/2 + i*sqrt(3)*(n^2/2 - i*sqrt(3)*n^2/2)^(1/3)/2)))*(m + ((n^2/2 - i*sqrt(3)*n^2/2)^(1/3)/2 - i*sqrt(3)*(n^2/2 - i*sqrt(3)*n^2/2)^(1/3)/2)))*(m + ((n^2/2 + i*sqrt(3)*n^2/2)^(1/3)/2 + i*sqrt(3)*(n^2/2 + i*sqrt(3)*n^2/2)^(1/3)/2)))*(m + ((n^2/2 + i*sqrt(3)*n^2/2)^(1/3)/2 - i*sqrt(3)*(n^2/2 + i*sqrt(3)*n^2/2)^(1/3)/2))