3 2
2 a 7*b*a
- 49*b + -- - 56*a*b - ------
8 64
$$\frac{a^{3}}{8} - \frac{7 a^{2} b}{64} - 56 a b - 49 b^{2}$$
-49*b^2 + a^3/8 - 56*a*b - 7*b*a^2/64
Разложение на множители
[src]
/ _________________________________________________________________________ \ / _________________________________________________________________________ \ / _________________________________________________________________________ \
| / ______________________________________________ | | / ______________________________________________ | | / ______________________________________________ |
| / / 2 3 | | / / 2 3 | | / / 2 3 |
| / / / 3\ / 2\ | | / / / 3\ / 2\ | | / / / 3\ / 2\ |
| / / | 2 343*b | | 49*b | | | / / | 2 343*b | | 49*b | | | / / | 2 343*b | | 49*b | |
| / / |- 14112*b - ------| - 4*|1344*b + -----| 3 2 | | / / |- 14112*b - ------| - 4*|1344*b + -----| 3 / ___\ 2 | | / / |- 14112*b - ------| - 4*|1344*b + -----| 3 / ___\ 2 |
| / \/ \ 256 / \ 64 / 2 343*b 49*b | | / \/ \ 256 / \ 64 / 2 343*b | 1 I*\/ 3 | 49*b | | / \/ \ 256 / \ 64 / 2 343*b | 1 I*\/ 3 | 49*b |
| 3 / ---------------------------------------------------- - 7056*b - ------ 1344*b + ----- | | 3 / ---------------------------------------------------- - 7056*b - ------ *|- - - -------| 1344*b + ----- | | 3 / ---------------------------------------------------- - 7056*b - ------ *|- - + -------| 1344*b + ----- |
| \/ 2 512 7*b 64 | | 7*b \/ 2 512 \ 2 2 / 64 | | 7*b \/ 2 512 \ 2 2 / 64 |
1*|a + ---------------------------------------------------------------------------------- - --- + ------------------------------------------------------------------------------------|*|a + - --- + -------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------|*|a + - --- + -------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------|
| 3 24 _________________________________________________________________________| | 24 3 _________________________________________________________________________| | 24 3 _________________________________________________________________________|
| / ______________________________________________ | | / ______________________________________________ | | / ______________________________________________ |
| / / 2 3 | | / / 2 3 | | / / 2 3 |
| / / / 3\ / 2\ | | / / / 3\ / 2\ | | / / / 3\ / 2\ |
| / / | 2 343*b | | 49*b | | | / / | 2 343*b | | 49*b | | | / / | 2 343*b | | 49*b | |
| / / |- 14112*b - ------| - 4*|1344*b + -----| 3 | | / ___\ / / |- 14112*b - ------| - 4*|1344*b + -----| 3 | | / ___\ / / |- 14112*b - ------| - 4*|1344*b + -----| 3 |
| / \/ \ 256 / \ 64 / 2 343*b | | | 1 I*\/ 3 | / \/ \ 256 / \ 64 / 2 343*b | | | 1 I*\/ 3 | / \/ \ 256 / \ 64 / 2 343*b |
| 3*3 / ---------------------------------------------------- - 7056*b - ------ | | 3*|- - - -------|*3 / ---------------------------------------------------- - 7056*b - ------ | | 3*|- - + -------|*3 / ---------------------------------------------------- - 7056*b - ------ |
\ \/ 2 512 / \ \ 2 2 / \/ 2 512 / \ \ 2 2 / \/ 2 512 /
$$1 \left(a + \left(- \frac{7 b}{24} + \frac{\sqrt[3]{- \frac{343 b^{3}}{512} - 7056 b^{2} + \frac{\sqrt{- 4 \left(\frac{49 b^{2}}{64} + 1344 b\right)^{3} + \left(- \frac{343 b^{3}}{256} - 14112 b^{2}\right)^{2}}}{2}}}{3} + \frac{\frac{49 b^{2}}{64} + 1344 b}{3 \sqrt[3]{- \frac{343 b^{3}}{512} - 7056 b^{2} + \frac{\sqrt{- 4 \left(\frac{49 b^{2}}{64} + 1344 b\right)^{3} + \left(- \frac{343 b^{3}}{256} - 14112 b^{2}\right)^{2}}}{2}}}\right)\right) \left(a + \left(- \frac{7 b}{24} + \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- \frac{343 b^{3}}{512} - 7056 b^{2} + \frac{\sqrt{- 4 \left(\frac{49 b^{2}}{64} + 1344 b\right)^{3} + \left(- \frac{343 b^{3}}{256} - 14112 b^{2}\right)^{2}}}{2}}}{3} + \frac{\frac{49 b^{2}}{64} + 1344 b}{3 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- \frac{343 b^{3}}{512} - 7056 b^{2} + \frac{\sqrt{- 4 \left(\frac{49 b^{2}}{64} + 1344 b\right)^{3} + \left(- \frac{343 b^{3}}{256} - 14112 b^{2}\right)^{2}}}{2}}}\right)\right) \left(a + \left(- \frac{7 b}{24} + \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- \frac{343 b^{3}}{512} - 7056 b^{2} + \frac{\sqrt{- 4 \left(\frac{49 b^{2}}{64} + 1344 b\right)^{3} + \left(- \frac{343 b^{3}}{256} - 14112 b^{2}\right)^{2}}}{2}}}{3} + \frac{\frac{49 b^{2}}{64} + 1344 b}{3 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- \frac{343 b^{3}}{512} - 7056 b^{2} + \frac{\sqrt{- 4 \left(\frac{49 b^{2}}{64} + 1344 b\right)^{3} + \left(- \frac{343 b^{3}}{256} - 14112 b^{2}\right)^{2}}}{2}}}\right)\right)$$
((1*(a + ((sqrt((-14112*b^2 - 343*b^3/256)^2 - 4*(1344*b + 49*b^2/64)^3)/2 - 7056*b^2 - 343*b^3/512)^(1/3)/3 - 7*b/24 + (1344*b + 49*b^2/64)/(3*(sqrt((-14112*b^2 - 343*b^3/256)^2 - 4*(1344*b + 49*b^2/64)^3)/2 - 7056*b^2 - 343*b^3/512)^(1/3)))))*(a - (7*b/24 + (sqrt((-14112*b^2 - 343*b^3/256)^2 - 4*(1344*b + 49*b^2/64)^3)/2 - 7056*b^2 - 343*b^3/512)^(1/3)*(-1/2 - i*sqrt(3)/2)/3 + (1344*b + 49*b^2/64)/(3*(-1/2 - i*sqrt(3)/2)*(sqrt((-14112*b^2 - 343*b^3/256)^2 - 4*(1344*b + 49*b^2/64)^3)/2 - 7056*b^2 - 343*b^3/512)^(1/3)))))*(a - (7*b/24 + (sqrt((-14112*b^2 - 343*b^3/256)^2 - 4*(1344*b + 49*b^2/64)^3)/2 - 7056*b^2 - 343*b^3/512)^(1/3)*(-1/2 + i*sqrt(3)/2)/3 + (1344*b + 49*b^2/64)/(3*(-1/2 + i*sqrt(3)/2)*(sqrt((-14112*b^2 - 343*b^3/256)^2 - 4*(1344*b + 49*b^2/64)^3)/2 - 7056*b^2 - 343*b^3/512)^(1/3))))
0.125*a^3 - 49.0*b^2 - 0.109375*b*a^2 - 56.0*a*b
0.125*a^3 - 49.0*b^2 - 0.109375*b*a^2 - 56.0*a*b
3 2
2 a 7*b*a
- 49*b + -- - 56*a*b - ------
8 64
$$\frac{a^{3}}{8} - \frac{7 a^{2} b}{64} - 56 a b - 49 b^{2}$$
3 / 2\
2 a | 7*a |
- 49*b + -- + b*|-56*a - ----|
8 \ 64 /
$$\frac{a^{3}}{8} - 49 b^{2} + b \left(- \frac{7 a^{2}}{64} - 56 a\right)$$
-49*b^2 + a^3/8 + b*(-56*a - 7*a^2/64)
Рациональный знаменатель
[src]
2 3 2
- 3136*b + 8*a - 3584*a*b - 7*b*a
------------------------------------
64
$$\frac{8 a^{3} - 7 a^{2} b - 3584 a b - 3136 b^{2}}{64}$$
3 2
2 a 7*b*a
- 49*b + -- - 56*a*b - ------
8 64
$$\frac{a^{3}}{8} - \frac{7 a^{2} b}{64} - 56 a b - 49 b^{2}$$
-49*b^2 + a^3/8 - 56*a*b - 7*b*a^2/64
3 2
2 a 7*b*a
- 49*b + -- - 56*a*b - ------
8 64
$$\frac{a^{3}}{8} - \frac{7 a^{2} b}{64} - 56 a b - 49 b^{2}$$
-49*b^2 + a^3/8 - 56*a*b - 7*b*a^2/64
3 2
2 a 7*b*a
- 49*b + -- - 56*a*b - ------
8 64
$$\frac{a^{3}}{8} - \frac{7 a^{2} b}{64} - 56 a b - 49 b^{2}$$
-49*b^2 + a^3/8 - 56*a*b - 7*b*a^2/64
3 2
2 a 7*b*a
- 49*b + -- - 56*a*b - ------
8 64
$$\frac{a^{3}}{8} - \frac{7 a^{2} b}{64} - 56 a b - 49 b^{2}$$
-49*b^2 + a^3/8 - 56*a*b - 7*b*a^2/64
Объединение рациональных выражений
[src]
2 3 2
- 3136*b + 8*a - 3584*a*b - 7*b*a
------------------------------------
64
$$\frac{8 a^{3} - 7 a^{2} b - 3584 a b - 3136 b^{2}}{64}$$
(-3136*b^2 + 8*a^3 - 3584*a*b - 7*b*a^2)/64