Mister Exam

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Factor polynomial:
x^3+27
x^2-x+5
p^9+64
x^6-x^4*y^2-x^3+x^2*y
Least common denominator:
(z+t)/(t-z)-(t-z)/(t+z)
(z/t-t/z)*5*t*z/z-t
(z*sqrt(z^2-a^2))/2-(a^2*log(2*sqrt(z^2-a^2)+2*z))/2
((z^2-z)/(z^2-9))^-1/(z^2-3*z)/(z-1)
Factor squared:
-y^4-y^2+1
-y^4+y^2+1
y^4+y^2+1
-y^4+y^2-10
How do you in partial fractions?:
(z-2)/(6*z+(z-2)*(z-2))+(6/(z*z*z-8))
2/(a+2)+(a-2)/(a^2+4*a+4)/(a/(2*a-4)+(a^2+4)/(8-2*a)-2/(2*a+a^2))
(z+1)/(z+2)^3/(z-1)
((4*x)^3*x^-11)/((x^-12)*(5*x^5))
Identical expressions
m^ three - twenty-seven *n^ three
m cubed minus 27 multiply by n cubed
m to the power of three minus twenty minus seven multiply by n to the power of three
m3-27*n3
m³-27*n³
m to the power of 3-27*n to the power of 3
m^3-27n^3
m3-27n3
Similar expressions
m^3+27*n^3

Expression simplification/ Factorization polynomials/ m^3-27*n^3

Factor polynomial m^3-27*n^3

The solution

You have entered [src]

 3       3
m  - 27*n

$$m^{3} - 27 n^{3}$$

m^3 - 27*n^3

Factorization [src]

          /        /          ___\\ /        /          ___\\
          |        |  1   I*\/ 3 || |        |  1   I*\/ 3 ||
(m - 3*n)*|m - 3*n*|- - - -------||*|m - 3*n*|- - + -------||
          \        \  2      2   // \        \  2      2   //

$$\left(m - 3 n\right) \left(m - 3 n \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right)\right) \left(m - 3 n \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right)\right)$$

((m - 3*n)*(m - 3*n*(-1/2 - i*sqrt(3)/2)))*(m - 3*n*(-1/2 + i*sqrt(3)/2))

Numerical answer [src]

m^3 - 27.0*n^3

m^3 - 27.0*n^3

Combinatorics [src]

          / 2      2        \
(m - 3*n)*\m  + 9*n  + 3*m*n/

$$\left(m - 3 n\right) \left(m^{2} + 3 m n + 9 n^{2}\right)$$

(m - 3*n)*(m^2 + 9*n^2 + 3*m*n)

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Factor polynomial m^3-27*n^3

The solution