Господин Экзамен
Разложить многочлен на множители 56*a^10*b^6-32*a^4*b^8
Решение
Вы ввели
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10 6 4 8 56*a *b - 32*a *b
$$56 a^{10} b^{6} - 32 a^{4} b^{8}$$
56*a^10*b^6 - 32*a^4*b^8
Общее упрощение
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4 6 / 2 6\ a *b *\- 32*b + 56*a /
$$a^{4} b^{6} \cdot \left(56 a^{6} - 32 b^{2}\right)$$
a^4*b^6*(-32*b^2 + 56*a^6)
Разложение на множители
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/ ____\ / ____\ / ____ ____\ / ____ ____\ / ____ ____\ / ____ ____\
| 3 ___ 5/6 6 / 2 | | 3 ___ 5/6 6 / 2 | | 3 ___ 5/6 6 / 2 3 ___ ___ 5/6 6 / 2 | | 3 ___ 5/6 6 / 2 3 ___ ___ 5/6 6 / 2 | | 3 ___ 5/6 6 / 2 3 ___ ___ 5/6 6 / 2 | | 3 ___ 5/6 6 / 2 3 ___ ___ 5/6 6 / 2 |
| \/ 2 *7 *\/ b | | \/ 2 *7 *\/ b | | \/ 2 *7 *\/ b I*\/ 2 *\/ 3 *7 *\/ b | | \/ 2 *7 *\/ b I*\/ 2 *\/ 3 *7 *\/ b | | \/ 2 *7 *\/ b I*\/ 2 *\/ 3 *7 *\/ b | | \/ 2 *7 *\/ b I*\/ 2 *\/ 3 *7 *\/ b |
1*(a + 0)*|a + ------------------|*|a - ------------------|*|a + ------------------ + --------------------------|*|a + ------------------ - --------------------------|*|a + - ------------------ + --------------------------|*|a + - ------------------ - --------------------------|*(b + 0)
\ 7 / \ 7 / \ 14 14 / \ 14 14 / \ 14 14 / \ 14 14 /
$$1 \left(a + 0\right) \left(a + \frac{\sqrt[3]{2} \cdot 7^{\frac{5}{6}} \sqrt[6]{b^{2}}}{7}\right) \left(a - \frac{\sqrt[3]{2} \cdot 7^{\frac{5}{6}} \sqrt[6]{b^{2}}}{7}\right) \left(a + \left(\frac{\sqrt[3]{2} \cdot 7^{\frac{5}{6}} \sqrt[6]{b^{2}}}{14} + \frac{\sqrt[3]{2} \sqrt{3} \cdot 7^{\frac{5}{6}} i \sqrt[6]{b^{2}}}{14}\right)\right) \left(a + \left(\frac{\sqrt[3]{2} \cdot 7^{\frac{5}{6}} \sqrt[6]{b^{2}}}{14} - \frac{\sqrt[3]{2} \sqrt{3} \cdot 7^{\frac{5}{6}} i \sqrt[6]{b^{2}}}{14}\right)\right) \left(a - \left(\frac{\sqrt[3]{2} \cdot 7^{\frac{5}{6}} \sqrt[6]{b^{2}}}{14} - \frac{\sqrt[3]{2} \sqrt{3} \cdot 7^{\frac{5}{6}} i \sqrt[6]{b^{2}}}{14}\right)\right) \left(a - \left(\frac{\sqrt[3]{2} \cdot 7^{\frac{5}{6}} \sqrt[6]{b^{2}}}{14} + \frac{\sqrt[3]{2} \sqrt{3} \cdot 7^{\frac{5}{6}} i \sqrt[6]{b^{2}}}{14}\right)\right) \left(b + 0\right)$$
(((((((1*(a + 0))*(a + 2^(1/3)*7^(5/6)*(b^2)^(1/6)/7))*(a - 2^(1/3)*7^(5/6)*(b^2)^(1/6)/7))*(a + (2^(1/3)*7^(5/6)*(b^2)^(1/6)/14 + i*2^(1/3)*sqrt(3)*7^(5/6)*(b^2)^(1/6)/14)))*(a + (2^(1/3)*7^(5/6)*(b^2)^(1/6)/14 - i*2^(1/3)*sqrt(3)*7^(5/6)*(b^2)^(1/6)/14)))*(a - (2^(1/3)*7^(5/6)*(b^2)^(1/6)/14 + i*2^(1/3)*sqrt(3)*7^(5/6)*(b^2)^(1/6)/14)))*(a - (2^(1/3)*7^(5/6)*(b^2)^(1/6)/14 - i*2^(1/3)*sqrt(3)*7^(5/6)*(b^2)^(1/6)/14)))*(b + 0)
Объединение рациональных выражений
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4 6 / 2 6\ 8*a *b *\- 4*b + 7*a /
$$8 a^{4} b^{6} \cdot \left(7 a^{6} - 4 b^{2}\right)$$
8*a^4*b^6*(-4*b^2 + 7*a^6)
Комбинаторика
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4 6 / 2 6\ 8*a *b *\- 4*b + 7*a /
$$8 a^{4} b^{6} \cdot \left(7 a^{6} - 4 b^{2}\right)$$
8*a^4*b^6*(-4*b^2 + 7*a^6)