Вынесите общий множитель за скобки 18*a^5-60*a^2*b+50*a*b^3 (18 умножить на a в степени 5 минус 60 умножить на a в квадрате умножить на b плюс 50 умножить на a умножить на b в кубе) контрольная работа по алгебре 7 класс [Есть ответ!]

Общий множитель 18*a^5-60*a^2*b+50*a*b^3

Учитель очень удивится увидев твоё верное решение😉

Решение

Комбинаторика [src]
    /   4       3         \
2*a*\9*a  + 25*b  - 30*a*b/
$$2 a \left(9 a^{4} - 30 a b + 25 b^{3}\right)$$
Разложение на множители [src]
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  |    ||          /         /      /    15625*b    625*b     25*b                         50*b                                 /                                                           27*3 /      /   - -------- + ------  + -----              /         /      /    15625*b    625*b     25*b                         50*b                                      || |    ||        /                                                           27*3 /      /   - -------- + ------  + -----              /         /      /    15625*b    625*b     25*b                         50*b                                  /         /      /    15625*b    625*b     25*b                         50*b                                     || |    ||        /         /      /    15625*b    625*b     25*b                         50*b                                 /                                                           27*3 /      /   - -------- + ------  + -----              /         /      /    15625*b    625*b     25*b                         50*b                                      || |    ||        /         /      /    15625*b    625*b     25*b                         50*b                                 /                                                           27*3 /      /   - -------- + ------  + -----              /         /      /    15625*b    625*b     25*b                         50*b                                      ||
  |    ||         /     2*3 /      /   - -------- + ------  + -----  + ---------------------------------------------           /                                                               \/     \/       19683      1296       36     3*       /     2*3 /      /   - -------- + ------  + -----  + ---------------------------------------------                 || |    ||       /                                                               \/     \/       19683      1296       36     3*       /     2*3 /      /   - -------- + ------  + -----  + ---------------------------------------------            /     2*3 /      /   - -------- + ------  + -----  + ---------------------------------------------                || |    ||       /     2*3 /      /   - -------- + ------  + -----  + ---------------------------------------------           /                                                               \/     \/       19683      1296       36     3*       /     2*3 /      /   - -------- + ------  + -----  + ---------------------------------------------                 || |    ||       /     2*3 /      /   - -------- + ------  + -----  + ---------------------------------------------           /                                                               \/     \/       19683      1296       36     3*       /     2*3 /      /   - -------- + ------  + -----  + ---------------------------------------------                 ||
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  |    ||     /                                                              /      /    15625*b    625*b     25*b         /                                                                                                                     /                                                              /      /    15625*b    625*b     25*b                   || |    ||   /                                                                                                                     /                                                              /      /    15625*b    625*b     25*b          /                                                              /      /    15625*b    625*b     25*b                  || |    ||   /                                                              /      /    15625*b    625*b     25*b         /                                                                                                                     /                                                              /      /    15625*b    625*b     25*b                   || |    ||   /                                                              /      /    15625*b    625*b     25*b         /                                                                                                                     /                                                              /      /    15625*b    625*b     25*b                   ||
  |    ||    /                                                         27*3 /      /   - -------- + ------  + -----       /                                                                                                                     /                                                         27*3 /      /   - -------- + ------  + -----                  || |    ||  /                                                                                                                     /                                                         27*3 /      /   - -------- + ------  + -----        /                                                         27*3 /      /   - -------- + ------  + -----                 || |    ||  /                                                         27*3 /      /   - -------- + ------  + -----       /                                                                                                                     /                                                         27*3 /      /   - -------- + ------  + -----                  || |    ||  /                                                         27*3 /      /   - -------- + ------  + -----       /                                                                                                                     /                                                         27*3 /      /   - -------- + ------  + -----                  ||
  |    ||  \/                                                             \/     \/       19683      1296       36      \/                                                                                                                    \/                                                             \/     \/       19683      1296       36                   || |    ||\/                                                                                                                    \/                                                             \/     \/       19683      1296       36       \/                                                             \/     \/       19683      1296       36                  || |    ||\/                                                             \/     \/       19683      1296       36      \/                                                                                                                    \/                                                             \/     \/       19683      1296       36                   || |    ||\/                                                             \/     \/       19683      1296       36      \/                                                                                                                    \/                                                             \/     \/       19683      1296       36                   ||
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  \    \\                                                                                                                                                                                                                                                                                                                                                               // \    \\                                                                                                                                                                                                                                                                                                                                                             // \    \\                                                                                                                                                                                                                                                                                                                                                             // \    \\                                                                                                                                                                                                                                                                                                                                                             //
$$a \left(a - \begin{cases} - \frac{\sqrt[3]{10} \cdot 3^{\frac{2}{3}} \sqrt{- \sqrt[3]{- b^{2}}}}{6} - \frac{\sqrt{- \frac{2 \cdot 10^{\frac{2}{3}} \sqrt[3]{3} b}{3 \sqrt{- \sqrt[3]{- b^{2}}}} + \frac{\sqrt[3]{12} \cdot 5^{\frac{2}{3}} \sqrt[3]{- b^{2}}}{3}}}{2} & \text{for}\: \frac{25 b^{3}}{9} = 0 \\- \frac{\sqrt{\frac{50 b^{3}}{27 \sqrt[3]{\frac{25 b^{2}}{36} + \sqrt{- \frac{15625 b^{9}}{19683} + \frac{625 b^{4}}{1296}}}} + 2 \sqrt[3]{\frac{25 b^{2}}{36} + \sqrt{- \frac{15625 b^{9}}{19683} + \frac{625 b^{4}}{1296}}}}}{2} - \frac{\sqrt{- \frac{50 b^{3}}{27 \sqrt[3]{\frac{25 b^{2}}{36} + \sqrt{- \frac{15625 b^{9}}{19683} + \frac{625 b^{4}}{1296}}}} - \frac{20 b}{3 \sqrt{\frac{50 b^{3}}{27 \sqrt[3]{\frac{25 b^{2}}{36} + \sqrt{- \frac{15625 b^{9}}{19683} + \frac{625 b^{4}}{1296}}}} + 2 \sqrt[3]{\frac{25 b^{2}}{36} + \sqrt{- \frac{15625 b^{9}}{19683} + \frac{625 b^{4}}{1296}}}}} - 2 \sqrt[3]{\frac{25 b^{2}}{36} + \sqrt{- \frac{15625 b^{9}}{19683} + \frac{625 b^{4}}{1296}}}}}{2} & \text{otherwise} \end{cases}\right) \left(a - \begin{cases} - \frac{\sqrt[3]{10} \cdot 3^{\frac{2}{3}} \sqrt{- \sqrt[3]{- b^{2}}}}{6} + \frac{\sqrt{- \frac{2 \cdot 10^{\frac{2}{3}} \sqrt[3]{3} b}{3 \sqrt{- \sqrt[3]{- b^{2}}}} + \frac{\sqrt[3]{12} \cdot 5^{\frac{2}{3}} \sqrt[3]{- b^{2}}}{3}}}{2} & \text{for}\: \frac{25 b^{3}}{9} = 0 \\- \frac{\sqrt{\frac{50 b^{3}}{27 \sqrt[3]{\frac{25 b^{2}}{36} + \sqrt{- \frac{15625 b^{9}}{19683} + \frac{625 b^{4}}{1296}}}} + 2 \sqrt[3]{\frac{25 b^{2}}{36} + \sqrt{- \frac{15625 b^{9}}{19683} + \frac{625 b^{4}}{1296}}}}}{2} + \frac{\sqrt{- \frac{50 b^{3}}{27 \sqrt[3]{\frac{25 b^{2}}{36} + \sqrt{- \frac{15625 b^{9}}{19683} + \frac{625 b^{4}}{1296}}}} - \frac{20 b}{3 \sqrt{\frac{50 b^{3}}{27 \sqrt[3]{\frac{25 b^{2}}{36} + \sqrt{- \frac{15625 b^{9}}{19683} + \frac{625 b^{4}}{1296}}}} + 2 \sqrt[3]{\frac{25 b^{2}}{36} + \sqrt{- \frac{15625 b^{9}}{19683} + \frac{625 b^{4}}{1296}}}}} - 2 \sqrt[3]{\frac{25 b^{2}}{36} + \sqrt{- \frac{15625 b^{9}}{19683} + \frac{625 b^{4}}{1296}}}}}{2} & \text{otherwise} \end{cases}\right) \left(a - \begin{cases} \frac{\sqrt[3]{10} \cdot 3^{\frac{2}{3}} \sqrt{- \sqrt[3]{- b^{2}}}}{6} - \frac{\sqrt{\frac{2 \cdot 10^{\frac{2}{3}} \sqrt[3]{3} b}{3 \sqrt{- \sqrt[3]{- b^{2}}}} + \frac{\sqrt[3]{12} \cdot 5^{\frac{2}{3}} \sqrt[3]{- b^{2}}}{3}}}{2} & \text{for}\: \frac{25 b^{3}}{9} = 0 \\\frac{\sqrt{\frac{50 b^{3}}{27 \sqrt[3]{\frac{25 b^{2}}{36} + \sqrt{- \frac{15625 b^{9}}{19683} + \frac{625 b^{4}}{1296}}}} + 2 \sqrt[3]{\frac{25 b^{2}}{36} + \sqrt{- \frac{15625 b^{9}}{19683} + \frac{625 b^{4}}{1296}}}}}{2} - \frac{\sqrt{- \frac{50 b^{3}}{27 \sqrt[3]{\frac{25 b^{2}}{36} + \sqrt{- \frac{15625 b^{9}}{19683} + \frac{625 b^{4}}{1296}}}} + \frac{20 b}{3 \sqrt{\frac{50 b^{3}}{27 \sqrt[3]{\frac{25 b^{2}}{36} + \sqrt{- \frac{15625 b^{9}}{19683} + \frac{625 b^{4}}{1296}}}} + 2 \sqrt[3]{\frac{25 b^{2}}{36} + \sqrt{- \frac{15625 b^{9}}{19683} + \frac{625 b^{4}}{1296}}}}} - 2 \sqrt[3]{\frac{25 b^{2}}{36} + \sqrt{- \frac{15625 b^{9}}{19683} + \frac{625 b^{4}}{1296}}}}}{2} & \text{otherwise} \end{cases}\right) \left(a - \begin{cases} \frac{\sqrt[3]{10} \cdot 3^{\frac{2}{3}} \sqrt{- \sqrt[3]{- b^{2}}}}{6} + \frac{\sqrt{\frac{2 \cdot 10^{\frac{2}{3}} \sqrt[3]{3} b}{3 \sqrt{- \sqrt[3]{- b^{2}}}} + \frac{\sqrt[3]{12} \cdot 5^{\frac{2}{3}} \sqrt[3]{- b^{2}}}{3}}}{2} & \text{for}\: \frac{25 b^{3}}{9} = 0 \\\frac{\sqrt{\frac{50 b^{3}}{27 \sqrt[3]{\frac{25 b^{2}}{36} + \sqrt{- \frac{15625 b^{9}}{19683} + \frac{625 b^{4}}{1296}}}} + 2 \sqrt[3]{\frac{25 b^{2}}{36} + \sqrt{- \frac{15625 b^{9}}{19683} + \frac{625 b^{4}}{1296}}}}}{2} + \frac{\sqrt{- \frac{50 b^{3}}{27 \sqrt[3]{\frac{25 b^{2}}{36} + \sqrt{- \frac{15625 b^{9}}{19683} + \frac{625 b^{4}}{1296}}}} + \frac{20 b}{3 \sqrt{\frac{50 b^{3}}{27 \sqrt[3]{\frac{25 b^{2}}{36} + \sqrt{- \frac{15625 b^{9}}{19683} + \frac{625 b^{4}}{1296}}}} + 2 \sqrt[3]{\frac{25 b^{2}}{36} + \sqrt{- \frac{15625 b^{9}}{19683} + \frac{625 b^{4}}{1296}}}}} - 2 \sqrt[3]{\frac{25 b^{2}}{36} + \sqrt{- \frac{15625 b^{9}}{19683} + \frac{625 b^{4}}{1296}}}}}{2} & \text{otherwise} \end{cases}\right)$$
Объединение рациональных выражений [src]
    /    3       /           3\\
2*a*\25*b  + 3*a*\-10*b + 3*a //
$$2 a \left(3 a \left(3 a^{3} - 10 b\right) + 25 b^{3}\right)$$
Общее упрощение [src]
    /   4       3         \
2*a*\9*a  + 25*b  - 30*a*b/
$$2 a \left(9 a^{4} - 30 a b + 25 b^{3}\right)$$
Собрать выражение [src]
    5         2         3
18*a  - 60*b*a  + 50*a*b 
$$18 a^{5} - 60 a^{2} b + 50 a b^{3}$$