Mister Exam

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Factor polynomial:
x^6-x^8
a*m^2+b*m^2-c*n-b*n+c*m^2-a*n
3*u^3-2*u*v^2-v^2-5*u^3+3*u*v^2+3*v^2
y^5-32
Least common denominator:
(x*(x-1)^2)^(1/3)*((x-1)^2/3+x*(-2+2*x)/3)/(x*(x-1)^2)
((x^3+y^3)/(x+y))/(x^2-y^2)+(2*y)/(x+y)-(x*y)/(x^2-y^2)
(x-1)*(1/(2*(x-1))-(x+1)/(2*(x-1)^2))/(x+1)
factorial(5)/(m*(m+1))*factorial(m+1)/factorial(m-1)
Factor squared:
y^4+y^2+9
-y^4-y^2+8
x^2-x*a+4*a^2
3*x^2+5*x-3
How do you in partial fractions?:
(5*a^2+3*a-2)/(a^2-1)
(u^2-4*u+16)/(16*u^2-1)*(4*u^2+u)/(u^3+64)
y/(b*y-2*b^2)-2/(y^2+y-2*b*y-2*b)*(1+(3*y+y^2)/(3+y))
(((2s-2+2*s^2)/(-s*(2+s^2+2*s)))+((-2s^2+2s-6))/((s*(s^2+2*s+2))))*1/s-2/s
Identical expressions
three *u^ three - two *u*v^ two -v^ two - five *u^ three + three *u*v^ two + three *v^ two
3 multiply by u cubed minus 2 multiply by u multiply by v squared minus v squared minus 5 multiply by u cubed plus 3 multiply by u multiply by v squared plus 3 multiply by v squared
three multiply by u to the power of three minus two multiply by u multiply by v to the power of two minus v to the power of two minus five multiply by u to the power of three plus three multiply by u multiply by v to the power of two plus three multiply by v to the power of two
3*u3-2*u*v2-v2-5*u3+3*u*v2+3*v2
3*u³-2*u*v²-v²-5*u³+3*u*v²+3*v²
3*u to the power of 3-2*u*v to the power of 2-v to the power of 2-5*u to the power of 3+3*u*v to the power of 2+3*v to the power of 2
3u^3-2uv^2-v^2-5u^3+3uv^2+3v^2
3u3-2uv2-v2-5u3+3uv2+3v2
Similar expressions
3*u^3-2*u*v^2-v^2-5*u^3-3*u*v^2+3*v^2
3*u^3-2*u*v^2-v^2+5*u^3+3*u*v^2+3*v^2
3*u^3+2*u*v^2-v^2-5*u^3+3*u*v^2+3*v^2
3*u^3-2*u*v^2+v^2-5*u^3+3*u*v^2+3*v^2
3*u^3-2*u*v^2-v^2-5*u^3+3*u*v^2-3*v^2

Expression simplification/ Factorization polynomials/ 3*u^3-2*u*v^2-v^2-5*u^3+3*u*v^2+3*v^2

Factor polynomial 3u^3-2uv^2-v^2-5u^3+3uv^2+3*v^2

The solution

You have entered [src]

   3        2    2      3        2      2
3*u  - 2*u*v  - v  - 5*u  + 3*u*v  + 3*v

$$3 v^{2} + \left(3 u v^{2} + \left(- 5 u^{3} + \left(- v^{2} + \left(3 u^{3} - 2 u v^{2}\right)\right)\right)\right)$$

3*u^3 - 2*u*v^2 - v^2 - 5*u^3 + (3*u)*v^2 + 3*v^2

General simplification [src]

     3      2      2
- 2*u  + 2*v  + u*v

$$- 2 u^{3} + u v^{2} + 2 v^{2}$$

-2*u^3 + 2*v^2 + u*v^2

Factorization [src]

/            _______________________________                                            \ /            _______________________________                                                                            \ /            _______________________________                                                                            \
|           /      ________________                                                     | |           /      ________________                                                                                     | |           /      ________________                                                                                     |
|          /      /              6                                                      | |          /      /              6                                                                                      | |          /      /              6                                                                                      |
|         /      /       4   27*v                                                       | |         /      /       4   27*v                                                                                       | |         /      /       4   27*v                                                                                       |
|        /      /   729*v  - -----        2                                             | |        /      /   729*v  - -----        2  /          ___\                                                            | |        /      /   729*v  - -----        2  /          ___\                                                            |
|       /     \/               2      27*v                                              | |       /     \/               2      27*v   |  1   I*\/ 3 |                                                            | |       /     \/               2      27*v   |  1   I*\/ 3 |                                                            |
|    3 /      --------------------- - -----                         2                   | |    3 /      --------------------- - ----- *|- - - -------|                                2                           | |    3 /      --------------------- - ----- *|- - + -------|                                2                           |
|    \/                 2               2                          v                    | |    \/                 2               2    \  2      2   /                               v                            | |    \/                 2               2    \  2      2   /                               v                            |
|u + --------------------------------------- + -----------------------------------------|*|u + ------------------------------------------------------- + ---------------------------------------------------------|*|u + ------------------------------------------------------- + ---------------------------------------------------------|
|                       3                                _______________________________| |                               3                                                        _______________________________| |                               3                                                        _______________________________|
|                                                       /      ________________         | |                                                                                       /      ________________         | |                                                                                       /      ________________         |
|                                                      /      /              6          | |                                                                                      /      /              6          | |                                                                                      /      /              6          |
|                                                     /      /       4   27*v           | |                                                                                     /      /       4   27*v           | |                                                                                     /      /       4   27*v           |
|                                                    /      /   729*v  - -----        2 | |                                                                /          ___\     /      /   729*v  - -----        2 | |                                                                /          ___\     /      /   729*v  - -----        2 |
|                                                   /     \/               2      27*v  | |                                                                |  1   I*\/ 3 |    /     \/               2      27*v  | |                                                                |  1   I*\/ 3 |    /     \/               2      27*v  |
|                                              2*3 /      --------------------- - ----- | |                                                              2*|- - - -------|*3 /      --------------------- - ----- | |                                                              2*|- - + -------|*3 /      --------------------- - ----- |
\                                                \/                 2               2   / \                                                                \  2      2   / \/                 2               2   / \                                                                \  2      2   / \/                 2               2   /

$$\left(u + \left(\frac{v^{2}}{2 \sqrt[3]{- \frac{27 v^{2}}{2} + \frac{\sqrt{- \frac{27 v^{6}}{2} + 729 v^{4}}}{2}}} + \frac{\sqrt[3]{- \frac{27 v^{2}}{2} + \frac{\sqrt{- \frac{27 v^{6}}{2} + 729 v^{4}}}{2}}}{3}\right)\right) \left(u + \left(\frac{v^{2}}{2 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- \frac{27 v^{2}}{2} + \frac{\sqrt{- \frac{27 v^{6}}{2} + 729 v^{4}}}{2}}} + \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- \frac{27 v^{2}}{2} + \frac{\sqrt{- \frac{27 v^{6}}{2} + 729 v^{4}}}{2}}}{3}\right)\right) \left(u + \left(\frac{v^{2}}{2 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- \frac{27 v^{2}}{2} + \frac{\sqrt{- \frac{27 v^{6}}{2} + 729 v^{4}}}{2}}} + \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- \frac{27 v^{2}}{2} + \frac{\sqrt{- \frac{27 v^{6}}{2} + 729 v^{4}}}{2}}}{3}\right)\right)$$

((u + (sqrt(729*v^4 - 27*v^6/2)/2 - 27*v^2/2)^(1/3)/3 + v^2/(2*(sqrt(729*v^4 - 27*v^6/2)/2 - 27*v^2/2)^(1/3)))*(u + (sqrt(729*v^4 - 27*v^6/2)/2 - 27*v^2/2)^(1/3)*(-1/2 - i*sqrt(3)/2)/3 + v^2/(2*(-1/2 - i*sqrt(3)/2)*(sqrt(729*v^4 - 27*v^6/2)/2 - 27*v^2/2)^(1/3))))*(u + (sqrt(729*v^4 - 27*v^6/2)/2 - 27*v^2/2)^(1/3)*(-1/2 + i*sqrt(3)/2)/3 + v^2/(2*(-1/2 + i*sqrt(3)/2)*(sqrt(729*v^4 - 27*v^6/2)/2 - 27*v^2/2)^(1/3)))

Numerical answer [src]

2.0*v^2 - 2.0*u^3 + 1.0*u*v^2

2.0*v^2 - 2.0*u^3 + 1.0*u*v^2

Combining rational expressions [src]

     3      2     /     2      2\        2
- 5*u  + 2*v  + u*\- 2*v  + 3*u / + 3*u*v

$$- 5 u^{3} + 3 u v^{2} + u \left(3 u^{2} - 2 v^{2}\right) + 2 v^{2}$$

-5*u^3 + 2*v^2 + u*(-2*v^2 + 3*u^2) + 3*u*v^2

Common denominator [src]

     3      2      2
- 2*u  + 2*v  + u*v

$$- 2 u^{3} + u v^{2} + 2 v^{2}$$

-2*u^3 + 2*v^2 + u*v^2

Combinatorics [src]

     3      2      2
- 2*u  + 2*v  + u*v

$$- 2 u^{3} + u v^{2} + 2 v^{2}$$

-2*u^3 + 2*v^2 + u*v^2

Assemble expression [src]

     3      2      2
- 2*u  + 2*v  + u*v

$$- 2 u^{3} + u v^{2} + 2 v^{2}$$

     3    2        
- 2*u  + v *(2 + u)

$$- 2 u^{3} + v^{2} \left(u + 2\right)$$

-2*u^3 + v^2*(2 + u)

Rational denominator [src]

     3      2      2
- 2*u  + 2*v  + u*v

$$- 2 u^{3} + u v^{2} + 2 v^{2}$$

-2*u^3 + 2*v^2 + u*v^2

Trigonometric part [src]

     3      2      2
- 2*u  + 2*v  + u*v

$$- 2 u^{3} + u v^{2} + 2 v^{2}$$

-2*u^3 + 2*v^2 + u*v^2

Powers [src]

     3      2      2
- 2*u  + 2*v  + u*v

$$- 2 u^{3} + u v^{2} + 2 v^{2}$$

-2*u^3 + 2*v^2 + u*v^2

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Identical expressions

Similar expressions

Factor polynomial 3*u^3-2*u*v^2-v^2-5*u^3+3*u*v^2+3*v^2

The solution

Factor polynomial 3u^3-2uv^2-v^2-5u^3+3uv^2+3*v^2