Вынесите общий множитель за скобки 4*b^9-12*b^3*c^2+9*c^4 (4 умножить на b в степени 9 минус 12 умножить на b в кубе умножить на c в квадрате плюс 9 умножить на c в степени 4) контрольная работа по алгебре 7 класс [Есть ответ!]

Общий множитель 4*b^9-12*b^3*c^2+9*c^4

Учитель очень удивится увидев твоё верное решение😉

Решение

Комбинаторика [src]
   9      4       3  2
4*b  + 9*c  - 12*b *c 
$$4 b^{9} - 12 b^{3} c^{2} + 9 c^{4}$$
Разложение на множители [src]
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|         \/                                              \/   \/  - 64*c  + 81*c   + 9*c   | |         \/                                              \/   \/  - 64*c  + 81*c   + 9*c                   \/                                              \/   \/  - 64*c  + 81*c   + 9*c   | |         \/                                              \/   \/  - 64*c  + 81*c   + 9*c                   \/                                              \/   \/  - 64*c  + 81*c   + 9*c   | |    \/         - 2*\/   \/  - 64*c  + 81*c   + 9*c   + 2*I*\/ 3 *\/   \/  - 64*c  + 81*c   + 9*c     - 2*\/   \/  - 64*c  + 81*c   + 9*c   + 2*I*\/ 3 *\/   \/  - 64*c  + 81*c   + 9*c     - 2*\/   \/  - 64*c  + 81*c   + 9*c   + 2*I*\/ 3 *\/   \/  - 64*c  + 81*c   + 9*c              \/         - 2*\/   \/  - 64*c  + 81*c   + 9*c   + 2*I*\/ 3 *\/   \/  - 64*c  + 81*c   + 9*c     - 2*\/   \/  - 64*c  + 81*c   + 9*c   + 2*I*\/ 3 *\/   \/  - 64*c  + 81*c   + 9*c     - 2*\/   \/  - 64*c  + 81*c   + 9*c   + 2*I*\/ 3 *\/   \/  - 64*c  + 81*c   + 9*c   | |    \/         - 2*\/   \/  - 64*c  + 81*c   + 9*c   + 2*I*\/ 3 *\/   \/  - 64*c  + 81*c   + 9*c     - 2*\/   \/  - 64*c  + 81*c   + 9*c   + 2*I*\/ 3 *\/   \/  - 64*c  + 81*c   + 9*c     - 2*\/   \/  - 64*c  + 81*c   + 9*c   + 2*I*\/ 3 *\/   \/  - 64*c  + 81*c   + 9*c              \/         - 2*\/   \/  - 64*c  + 81*c   + 9*c   + 2*I*\/ 3 *\/   \/  - 64*c  + 81*c   + 9*c     - 2*\/   \/  - 64*c  + 81*c   + 9*c   + 2*I*\/ 3 *\/   \/  - 64*c  + 81*c   + 9*c     - 2*\/   \/  - 64*c  + 81*c   + 9*c   + 2*I*\/ 3 *\/   \/  - 64*c  + 81*c   + 9*c   | |    \/           2*\/   \/  - 64*c  + 81*c   + 9*c   + 2*I*\/ 3 *\/   \/  - 64*c  + 81*c   + 9*c     2*\/   \/  - 64*c  + 81*c   + 9*c   + 2*I*\/ 3 *\/   \/  - 64*c  + 81*c   + 9*c     2*\/   \/  - 64*c  + 81*c   + 9*c   + 2*I*\/ 3 *\/   \/  - 64*c  + 81*c   + 9*c              \/           2*\/   \/  - 64*c  + 81*c   + 9*c   + 2*I*\/ 3 *\/   \/  - 64*c  + 81*c   + 9*c     2*\/   \/  - 64*c  + 81*c   + 9*c   + 2*I*\/ 3 *\/   \/  - 64*c  + 81*c   + 9*c     2*\/   \/  - 64*c  + 81*c   + 9*c   + 2*I*\/ 3 *\/   \/  - 64*c  + 81*c   + 9*c   | |    \/           2*\/   \/  - 64*c  + 81*c   + 9*c   + 2*I*\/ 3 *\/   \/  - 64*c  + 81*c   + 9*c     2*\/   \/  - 64*c  + 81*c   + 9*c   + 2*I*\/ 3 *\/   \/  - 64*c  + 81*c   + 9*c     2*\/   \/  - 64*c  + 81*c   + 9*c   + 2*I*\/ 3 *\/   \/  - 64*c  + 81*c   + 9*c              \/           2*\/   \/  - 64*c  + 81*c   + 9*c   + 2*I*\/ 3 *\/   \/  - 64*c  + 81*c   + 9*c     2*\/   \/  - 64*c  + 81*c   + 9*c   + 2*I*\/ 3 *\/   \/  - 64*c  + 81*c   + 9*c     2*\/   \/  - 64*c  + 81*c   + 9*c   + 2*I*\/ 3 *\/   \/  - 64*c  + 81*c   + 9*c   | |          /                              \\/  - 64*c  + 81*c   + 9*c /                                                                       8*c                                                                 I*\/ 3 *\\/  - 64*c  + 81*c   + 9*c /                         | |          /                               \\/  - 64*c  + 81*c   + 9*c /                                                                     8*c                                                               I*\/ 3 *\\/  - 64*c  + 81*c   + 9*c /                        |
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$$\left(b - \frac{2^{\frac{2}{3}} \sqrt[3]{- \frac{4 c^{2}}{\sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}}} - \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}}}}{2}\right) \left(b + \left(\frac{2^{\frac{2}{3}} \sqrt[3]{- \frac{4 c^{2}}{\sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}}} - \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}}}}{4} + \frac{2^{\frac{2}{3}} \sqrt{3} i \sqrt[3]{- \frac{4 c^{2}}{\sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}}} - \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}}}}{4}\right)\right) \left(b + \left(\frac{2^{\frac{2}{3}} \sqrt[3]{- \frac{4 c^{2}}{\sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}}} - \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}}}}{4} - \frac{2^{\frac{2}{3}} \sqrt{3} i \sqrt[3]{- \frac{4 c^{2}}{\sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}}} - \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}}}}{4}\right)\right) \left(b + \left(\frac{\sqrt[3]{- \frac{8 c^{2}}{- 2 \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}} + 2 \sqrt{3} i \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}}} + \frac{\left(9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}\right)^{\frac{2}{3}}}{- 2 \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}} + 2 \sqrt{3} i \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}}} + \frac{\sqrt{3} i \left(9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}\right)^{\frac{2}{3}}}{- 2 \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}} + 2 \sqrt{3} i \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}}}}}{2} + \frac{\sqrt{3} i \sqrt[3]{- \frac{8 c^{2}}{- 2 \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}} + 2 \sqrt{3} i \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}}} + \frac{\left(9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}\right)^{\frac{2}{3}}}{- 2 \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}} + 2 \sqrt{3} i \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}}} + \frac{\sqrt{3} i \left(9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}\right)^{\frac{2}{3}}}{- 2 \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}} + 2 \sqrt{3} i \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}}}}}{2}\right)\right) \left(b + \left(\frac{\sqrt[3]{- \frac{8 c^{2}}{- 2 \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}} + 2 \sqrt{3} i \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}}} + \frac{\left(9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}\right)^{\frac{2}{3}}}{- 2 \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}} + 2 \sqrt{3} i \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}}} + \frac{\sqrt{3} i \left(9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}\right)^{\frac{2}{3}}}{- 2 \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}} + 2 \sqrt{3} i \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}}}}}{2} - \frac{\sqrt{3} i \sqrt[3]{- \frac{8 c^{2}}{- 2 \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}} + 2 \sqrt{3} i \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}}} + \frac{\left(9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}\right)^{\frac{2}{3}}}{- 2 \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}} + 2 \sqrt{3} i \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}}} + \frac{\sqrt{3} i \left(9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}\right)^{\frac{2}{3}}}{- 2 \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}} + 2 \sqrt{3} i \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}}}}}{2}\right)\right) \left(b + \left(\frac{\sqrt[3]{\frac{8 c^{2}}{2 \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}} + 2 \sqrt{3} i \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}}} - \frac{\left(9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}\right)^{\frac{2}{3}}}{2 \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}} + 2 \sqrt{3} i \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}}} + \frac{\sqrt{3} i \left(9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}\right)^{\frac{2}{3}}}{2 \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}} + 2 \sqrt{3} i \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}}}}}{2} + \frac{\sqrt{3} i \sqrt[3]{\frac{8 c^{2}}{2 \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}} + 2 \sqrt{3} i \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}}} - \frac{\left(9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}\right)^{\frac{2}{3}}}{2 \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}} + 2 \sqrt{3} i \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}}} + \frac{\sqrt{3} i \left(9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}\right)^{\frac{2}{3}}}{2 \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}} + 2 \sqrt{3} i \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}}}}}{2}\right)\right) \left(b + \left(\frac{\sqrt[3]{\frac{8 c^{2}}{2 \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}} + 2 \sqrt{3} i \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}}} - \frac{\left(9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}\right)^{\frac{2}{3}}}{2 \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}} + 2 \sqrt{3} i \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}}} + \frac{\sqrt{3} i \left(9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}\right)^{\frac{2}{3}}}{2 \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}} + 2 \sqrt{3} i \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}}}}}{2} - \frac{\sqrt{3} i \sqrt[3]{\frac{8 c^{2}}{2 \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}} + 2 \sqrt{3} i \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}}} - \frac{\left(9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}\right)^{\frac{2}{3}}}{2 \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}} + 2 \sqrt{3} i \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}}} + \frac{\sqrt{3} i \left(9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}\right)^{\frac{2}{3}}}{2 \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}} + 2 \sqrt{3} i \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}}}}}{2}\right)\right) \left(b - \sqrt[3]{- \frac{8 c^{2}}{- 2 \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}} + 2 \sqrt{3} i \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}}} + \frac{\left(9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}\right)^{\frac{2}{3}}}{- 2 \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}} + 2 \sqrt{3} i \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}}} + \frac{\sqrt{3} i \left(9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}\right)^{\frac{2}{3}}}{- 2 \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}} + 2 \sqrt{3} i \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}}}}\right) \left(b - \sqrt[3]{\frac{8 c^{2}}{2 \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}} + 2 \sqrt{3} i \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}}} - \frac{\left(9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}\right)^{\frac{2}{3}}}{2 \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}} + 2 \sqrt{3} i \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}}} + \frac{\sqrt{3} i \left(9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}\right)^{\frac{2}{3}}}{2 \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}} + 2 \sqrt{3} i \sqrt[3]{9 c^{4} + \sqrt{81 c^{8} - 64 c^{6}}}}}\right)$$
Объединение рациональных выражений [src]
   4      3 / 6      2\
9*c  + 4*b *\b  - 3*c /
$$4 b^{3} \left(b^{6} - 3 c^{2}\right) + 9 c^{4}$$
Собрать выражение [src]
   9      4       3  2
4*b  + 9*c  - 12*b *c 
$$4 b^{9} - 12 b^{3} c^{2} + 9 c^{4}$$
Общее упрощение [src]
   9      4       3  2
4*b  + 9*c  - 12*b *c 
$$4 b^{9} - 12 b^{3} c^{2} + 9 c^{4}$$